References

• [AGM94] S. Abramsky, D. M. Gabbay, T. S. E. Maibaum, editors. Handbook of logic in computer science. Vol. 3: Semantic structures. Oxford: Clarendon Press, 1994. ISBN 0-19-853762-X. Zbl:0829.68111. [1] [2] [3]
• [ARV10] J. Adámek, J. Rosický, E. M. Vitale. Algebraic Theories: A Categorical Introduction to General Algebra. Cambridge Tracts in Mathematics. Cambridge University Press, 2010. [1]
• [AL19] Benedikt Ahrens, Peter LeFanu Lumsdaine. Displayed Categories. Logical Methods in Computer Science, 2019. doi:10.23638/LMCS-15(1:20)2019. [1]
• [Aig97] Martin Aigner. Combinatorial theory. Classics in Mathematics. Springer-Verlag, Berlin, 1997. ISBN 3-540-61787-6. Reprint of the 1979 original. doi:10.1007/978-3-642-59101-3, MR:1434477, URL: https://doi.org/10.1007/978-3-642-59101-3. [1]
• [AZ98] Martin Aigner, Günter M. Ziegler. Proofs from THE BOOK. Berlin: Springer, 1998. ISBN 3-540-63698-6. Zbl:0905.00001. [1] [2]
• [AHCF12] Elad Aigner-Horev, Johannes Carmesin, Jan-Oliver Fröhlich. Infinite matroid union. 2012. arXiv:1111.0602. [1] [2]
• [AE72] Erik M. Alfsen, Edward G. Effros. Structure in real Banach spaces. I and II. Ann. Math. (2), 96:98–173, 1972. doi:10.2307/1970895, Zbl:0248.46019. [1]
• [AS03] Erik M. Alfsen, Frederic W. Shultz. Geometry of state spaces of operator algebras. Boston, MA: Birkhäuser, 2003. ISBN 0-8176-4319-2. Zbl:1042.46001. [1]
• [AK21] A. Altman, S. Kleiman. A Term of Commutative Algebra. Worldwide Center of Mathematics, 2021. ISBN 9780988557215. [1] [2] [3] [4] [5] [6] [7]
• [Alu16] Paolo Aluffi. Algebra: Chapter 0. Reprinted with corrections by the American Mathematical Society edition. Volume 104 of Graduate Studies in Mathematics. American Mathematical Society, 2016. [1]
• [AM69] M. F. Atiyah, I. G. Macdonald. Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR:0242802. [1] [2] [3] [4] [5]
• [ACH19] Jeremy Avigad, Mario M. Carneiro, Simon Hudon. Data Types as Quotients of Polynomial Functors. In John Harrison, John O'Leary, Andrew Tolmach, editors, 10th International Conference on Interactive Theorem Proving, ITP 2019, September 9-12, 2019, Portland, OR, USA, volume 141 of LIPIcs, 6:1–6:19. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. doi:10.4230/LIPIcs.ITP.2019.6, URL: https://doi.org/10.4230/LIPIcs.ITP.2019.6. [1] [2] [3] [4] [5] [6] [7] [8]
• [AdMK17] Jeremy Avigad, Leonardo de Moura, Soonho Kong. Theorem Proving in Lean. 2017. URL: https://leanprover.github.io/theorem_proving_in_lean/. [1]
• [Axl15] Sheldon Axler. Linear algebra done right. 3rd ed. 3rd ed. Springer, 2015. ISBN 978-3-319-11079-0/hbk; 978-3-319-11080-6/ebook. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
• [Ban] Banasiak. Banach Lattices in Applications. University of Pretoria, Pretoria, South Africa. [1] [2]
• [Bar67] Donald W. Barnes. On Cartan subalgebras of Lie algebras. Math. Z., 101:350–355, 1967. doi:10.1007/BF01109800, MR:220785, URL: https://doi.org/10.1007/BF01109800. [1] [2] [3] [4] [5] [6]
• [BH19] Clark Barwick, Peter Haine. Pyknotic objects, I. Basic notions. 2019. arXiv:1904.09966. [1]
• [Bas73] Hyman Bass. Unitary algebraic K-theory. In Hyman Bass, editor, Hermitian K-Theory and Geometric Applications, 57–265. Berlin, Heidelberg, 1973. Springer Berlin Heidelberg. [1]
• [Bea04] Richard Beals. Analysis. An introduction. Cambridge University Press, 2004. ISBN 0521600472.
• [BW93] Thomas Becker, Volker Weispfenning. Gröbner Bases. Volume 141 of Graduate Texts in Mathematics. Springer New York, New York, NY, 1993. ISBN 978-1-4612-6944-1. doi:10.1007/978-1-4612-0913-3, URL: http://link.springer.com/10.1007/978-1-4612-0913-3. [1]
• [Beh79] Ehrhard Behrends. M-structure and the Banach-Stone theorem. Volume 736. Springer, Cham, 1979. Zbl:0436.46013. [1]
• [BBDG18] A. A. Beilinson, J. Bernstein, P. Deligne, O. Gabber. Analyse et topologie sur les espaces singuliers. I : Faisceaux pervers. Volume 100 of Astérisque. Société Mathématique de France, Paris, 2018. MR:751965. [1]
• [Bel64] J. S. Bell. On the Einstein Podolsky Rosen paradox. Phys. Phys. Fiz., 1(3):195–200, 1964. doi:10.1103/PhysicsPhysiqueFizika.1.195, MR:3790629, URL: https://doi.org/10.1103/PhysicsPhysiqueFizika.1.195. [1]
• [Ber85] Vitaly Bergelson. Sets of Recurrence of Zm-Actions and Properties of Sets of Differences in Zm. Journal of the London Mathematical Society, s2-31(2):295-304, 1985. doi:10.1112/jlms/s2-31.2.295, URL: https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/jlms/s2-31.2.295, URL: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms/s2-31.2.295. [1]
• [Ber87] Marcel Berger. Geometry I. First edition. Universitext. Springer Berlin, Heidelberg, 1987. [1]
• [BL76] Jöran Bergh, Jörgen Löfström. Interpolation Spaces. Springer Berlin, 1976. [1]
• [Ber12] S. Bernstein. Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités. Comm. Kharkov Math. Soc., 1912.
• [Ber74] Pierre Berthelot. Cohomologie Cristalline Des Schémas de Caractéristique $p>0$. Number 407 in Lecture Notes in Mathematics. sv, 1974. [1] [2] [3]
• [BO78] Pierre Berthelot, Arthur Ogus. Notes on Crystalline Cohomology. Number 21 in Math. Notes. pup, 1978. [1]
• [BD96] Ilya Beylin, Peter Dybjer. Extracting a proof of coherence for monoidal categories from a proof of normalization for monoids. In Stefano Berardi, Mario Coppo, editors, Types for Proofs and Programs, 47–61. Berlin, Heidelberg, 1996. Springer Berlin Heidelberg. [1] [2]
• [Bil99] Patrick Billingsley. Convergence of probability measures. Second edition. Wiley Series in Probability and Statistics: Probability and Statistics. John Wiley & Sons, Inc., New York, 1999. ISBN 0-471-19745-9. A Wiley-Interscience Publication. doi:10.1002/9780470316962, MR:1700749, URL: https://doi.org/10.1002/9780470316962. [1] [2] [3] [4]
• [Bir37] Garrett Birkhoff. Rings of sets. Duke Mathematical Journal, 3(3):443–454, 1937. doi:10.1215/S0012-7094-37-00334-X, URL: https://doi.org/10.1215/S0012-7094-37-00334-X. [1]
• [Bir42] Garrett Birkhoff. Lattice-Ordered groups. Ann. of Math. (2), 43:298–331, 1942. doi:10.2307/1968871, MR:6550, URL: https://doi.org/10.2307/1968871. [1] [2] [3] [4]
• [BB05] Anders Björner, Francesco Brenti. Combinatorics of Coxeter groups. Volume 231 of Graduate Texts in Mathematics. Springer, New York, 2005. ISBN 978-3540-442387; 3-540-44238-3. MR:2133266.
• [Bla92] Andreas Blass. A game semantics for linear logic. Ann. Pure Appl. Logic, 56(1-3):183–220, 1992. doi:10.1016/0168-0072(92)90073-9, MR:1167694, URL: https://doi.org/10.1016/0168-0072(92)90073-9. [1]
• [Bog07] V. I. Bogachev. Measure theory. Vol. I, II. Springer-Verlag, Berlin, 2007. ISBN 978-3-540-34513-8; 3-540-34513-2. doi:10.1007/978-3-540-34514-5, URL: https://doi.org/10.1007/978-3-540-34514-5. [1]
• [Boj74] Ranko Bojanić. A simple proof of Mahler's theorem on approximation of continuous functions of a p-adic variable by polynomials. Journal of Number Theory, 6:412-415, 1974. doi:10.1016/0022-314X(74)90038-9, URL: https://doi.org/10.1016/0022-314X(74)90038-9. [1] [2]
• [Bol86] Béla Bollobás. Combinatorics: Set Systems, Hypergraphs, Families of Vectors, and Combinatorial Probability. Cambridge University Press, 1986. ISBN 0521330599. [1] [2]
• [Bor94a] Francis Borceux. Handbook of Categorical Algebra: Volume 1, Basic Category Theory. Volume 50 of Encyclopedia of Mathematics. Cambridge University Press, 1994. [1] [2] [3] [4]
• [Bor94b] Francis Borceux. Handbook of Categorical Algebra: Volume 2, Categories and Structures. Volume 51 of Encyclopedia of Mathematics. Cambridge University Press, 1994. [1] [2] [3] [4] [5] [6] [7] [8]
• [Bor94c] Francis Borceux. Handbook of Categorical Algebra: Volume 3, Sheaf Theory. Volume 52 of Encyclopedia of Mathematics. Cambridge University Press, 1994. [1] [2] [3]
• [Bor86] Richard Borcherds. Vertex algebras, Kac-Moody algebras, and the monster. Proceedings of the National Academy of Sciences of the United States of America, 83(10):3068–3071, 1986. doi:10.1073/pnas.83.10.3068. [1]
• [BGR84] S. Bosch, U. Güntzer, R. Remmert. Non-Archimedean Analysis : A Systematic Approach to Rigid Analytic Geometry. Volume 261 of Grundlehren der mathematischen Wissenschaften. Springer-Verlag Berlin, 1984. [1] [2] [3] [4] [5] [6] [7] [8] [9]
• [Bou87] N. Bourbaki. Topological vector spaces. Chapters 1–5. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 1987. ISBN 3-540-13627-4. Translated from the French by H. G. Eggleston and S. Madan. doi:10.1007/978-3-642-61715-7, MR:910295, URL: https://doi.org/10.1007/978-3-642-61715-7. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
• [Bou90] N. Bourbaki. Algebra. II. Chapters 4–7. Elements of Mathematics. Springer-Verlag, Berlin, 1990. ISBN 3-540-19375-8. Translated from the French by P. M. Cohn and J. Howie. MR:1080964. [1] [2] [3] [4] [5] [6] [7]
• [Bou98a] N. Bourbaki. Algebra. I. Chapters 1–3. Softcover edition of the 2nd printing 1989. Elements of Mathematics. Springer-Verlag, Berlin, 1998. ISBN 3-540-64243-9. Translated from the French. [1] [2] [3] [4]
• [Bou23] N. Bourbaki. Théories Spectrales. Chapitres 3 à 5. Number 1 in Éléments de mathématique. Springer Cham, 2023. ISBN 978-3-031-19504-4. URL: https://doi.org/10.1007/978-3-031-19505-1. [1]
• [Bou66a] Nicolas Bourbaki. Elements of mathematics. General topology. Part 1. Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR:0205210. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15]
• [Bou66b] Nicolas Bourbaki. Elements of mathematics. General topology. Part 2. Hermann, Paris; Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. MR:979295. [1] [2] [3] [4]
• [Bou98b] Nicolas Bourbaki. Lie groups and Lie algebras. Chapters 1–3. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 1998. ISBN 3-540-64242-0. Translated from the French, Reprint of the 1989 English translation. MR:1728312.
• [Bou02] Nicolas Bourbaki. Lie groups and Lie algebras. Chapters 4–6. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 2002. ISBN 3-540-42650-7. Translated from the 1968 French original by Andrew Pressley. MR:1890629. [1] [2] [3] [4] [5] [6] [7]
• [Bou05] Nicolas Bourbaki. Lie groups and Lie algebras. Chapters 7–9. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 2005. ISBN 3-540-43405-4. Translated from the 1975 and 1982 French originals by Andrew Pressley. MR:2109105.
• [Bou07] Nicolas Bourbaki. Algèbre. Chapitre IX. Réimpression inchangée de l'édition originale de 1959. Number 2 in Eléments de mathématique. Springer, 2007. ISBN 978-3-540-35338-6. [1] [2] [3] [4]
• [BG15] Nathan Bowler, Stefan Geschke. Self-dual uniform matroids on infinite sets. Proceedings of the American Mathematical Society, 144:1, Oct 2015. doi:10.1090/proc/12667.
• [BV04] Stephen P. Boyd, Lieven Vandenberghe. Convex Optimization. Cambridge University Press, 2004. ISBN 978-0-521-83378-3. URL: https://web.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf. [1]
• [BS13] M. P. Brodmann, R. Y. Sharp. Local cohomology. Second edition. Volume 136 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2013. ISBN 978-0-521-51363-0. An algebraic introduction with geometric applications. [1]
• [BDK+13] Henning Bruhn, Reinhard Diestel, Matthias Kriesell, Rudi Pendavingh, Paul Wollan. Axioms for infinite matroids. Advances in Mathematics, 239:18-46, 2013. doi:10.1016/j.aim.2013.01.011, URL: https://www.sciencedirect.com/science/article/pii/S0001870813000261.
• [Buz01] Raushan Z. Buzyakova. On clopen sets in Cartesian products. Comment. Math. Univ. Carolin., 42(2):357–362, 2001. MR:1832154. [1] [2] [3]
• [CGRP14] Miguel Cabrera García, Ángel Rodríguez Palacios. Non-associative normed algebras. Volume 1. The Vidav-Palmer and Gelfand-Naimark theorems. Volume 154. Cambridge: Cambridge University Press, 2014. ISBN 978-1-107-04306-0; 978-1-107-33776-3. doi:10.1017/CBO9781107337763, Zbl:1322.46003. [1] [2] [3]
• [CM72] Jean Marie Cadiou Cadiou, Zohar Manna. Recursive definitions of partial functions and their computations. ACM SIGACT News, pages 58–65, Jan 1972. doi:10.1145/942580.807072. [1]
• [Cal00] Grigore Cǎlugǎreanu. Lattice Concepts of Module Theory. Jan 2000. doi:10.1007/978-94-015-9588-9. [1] [2] [3] [4]
• [Car20] Olivia Caramello. Denseness conditions, morphisms and equivalences of toposes. 2020. arXiv:1906.08737, URL: https://arxiv.org/abs/1906.08737. [1]
• [CLW93] Aurelio Carboni, Stephen Lack, R.F.C. Walters. Introduction to extensive and distributive categories. Journal of Pure and Applied Algebra, 84(2):145-158, 1993. doi:10.1016/0022-4049(93)90035-R, URL: https://www.sciencedirect.com/science/article/pii/002240499390035R. [1]
• [Car15] Mario Carneiro. Arithmetic in Metamath, Case Study: Bertrand's Postulate. arXiv preprint arXiv:1503.02349, 2015. [1]
• [Car18] Mario Carneiro. A Lean formalization of Matiyasevič's theorem. 2018. arXiv:1802.01795. [1] [2]
• [Car19] Mario M. Carneiro. Formalizing Computability Theory via Partial Recursive Functions. In John Harrison, John O'Leary, Andrew Tolmach, editors, 10th International Conference on Interactive Theorem Proving, ITP 2019, September 9-12, 2019, Portland, OR, USA, volume 141 of LIPIcs, 12:1–12:17. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2019. doi:10.4230/LIPIcs.ITP.2019.12, URL: https://doi.org/10.4230/LIPIcs.ITP.2019.12. [1] [2] [3] [4]
• [Car05] R. W. Carter. Lie algebras of finite and affine type. Volume 96 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2005. ISBN 978-0-521-85138-1; 0-521-85138-6. doi:10.1017/CBO9780511614910, MR:2188930, URL: https://doi.org/10.1017/CBO9780511614910. [1] [2]
• [Cas50] J. W. S. Cassels. Some metrical theorems in Diophantine approximation. I. Proc. Cambridge Philos. Soc., 46:209–218, 1950. doi:10.1017/s0305004100025676, MR:36787, URL: https://doi.org/10.1017/s0305004100025676.
• [Cas86] J. W. S. Cassels. Local Fields. London Mathematical Society Student Texts. Cambridge University Press, 1986. doi:10.1017/CBO9781139171885. [1]
• [CF67] John William Scott Cassels, Albrecht Fröhlich. Algebraic number theory. Academic Press, London; Thompson Book Co., Inc., Washington, D.C., 1967. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
• [Cha96] Robin Chapman. A Polynomial Taking Integer Values. Math. Mag., 69(2):121–121, 1996.
• [Chi20] Vineeth Chintala. Sorry, the Nilpotents Are in the Center. Jun 2020. doi:10.48550/arXiv.1805.11451, arXiv:1805.11451. [1]
• [Cho94] Ching-Tsun Chou. A formal theory of undirected graphs in higher-order logic. In Thomas F. Melham, Juanito Camilleri, editors, Higher Order Logic Theorem Proving and Its Applications, 144–157. Berlin, Heidelberg, 1994. Springer Berlin Heidelberg. [1] [2] [3]
• [Chu12] Cho-Ho Chu. Jordan structures in geometry and analysis. Volume 190. Cambridge: Cambridge University Press, 2012. ISBN 978-1-107-01617-0. Zbl:1238.17001. [1]
• [Cir80] B. S. Cirelʹson. Quantum generalizations of Bell's inequality. Lett. Math. Phys., 4(2):93–100, 1980. doi:10.1007/BF00417500, MR:577178, URL: https://doi.org/10.1007/BF00417500. [1]
• [Cla] Pete L. Clark. Geometry of Numbers with Applications to Number Theory. URL: http://alpha.math.uga.edu/~pete/geometryofnumbers.pdf. [1]
• [CHSH69] John F. Clauser, Michael A. Horne, Abner Shimony, Richard A. Holt. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett., 23:880–883, 1969. doi:10.1103/PhysRevLett.23.880, Zbl:1371.81014, URL: https://doi.org/10.1103/PhysRevLett.23.880. [1]
• [CCC+12] David A. Cohen, Martin C. Cooper, Páidí Creed, Peter G. Jeavons, Stanislav Živný. An Algebraic Theory of Complexity for Discrete Optimisation. CoRR, 2012. arXiv:1207.6692, URL: http://arxiv.org/abs/1207.6692. [1]
• [Coh95] P. M. Cohn. Skew Fields: Theory of General Division Rings. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1995. doi:10.1017/CBO9781139087193. [1]
• [Col10] Pierre Colmez. Fonctions d'une variable p-adique. Asterisque, 330:13–59, 2010. URL: http://www.numdam.org/article/AST_2010__330__13_0.pdf. [1] [2]
• [CL21] Johan Commelin, Robert Y. Lewis. Formalizing the Ring of Witt Vectors. In Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2021, 264–277. New York, NY, USA, 2021. Association for Computing Machinery. doi:10.1145/3437992.3439919, URL: https://doi.org/10.1145/3437992.3439919. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
• [Con00] Brian Conrad. Grothendieck duality and base change. Volume 1750 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2000. ISBN 3-540-41134-8. doi:10.1007/b75857, MR:1804902, URL: https://doi.org/10.1007/b75857. [1] [2] [3] [4] [5] [6]
• [Cona] K. Conrad. Ostrowski for number fields. URL: https://kconrad.math.uconn.edu/blurbs/gradnumthy/ostrowskinumbfield.pdf. [1]
• [Conb] K. Conrad. Ostrowski's Theorem for Q. URL: https://kconrad.math.uconn.edu/blurbs/gradnumthy/ostrowskiQ.pdf. [1]
• [Con01] J. H. Conway. On numbers and games. Second edition. A K Peters, Ltd., Natick, MA, 2001. ISBN 1-56881-127-6. MR:1803095. [1] [2] [3]
• [Con90] John B. Conway. A course in functional analysis. 2nd ed. Volume 96 of Grad. Texts Math. New York etc.: Springer-Verlag, 1990. ISBN 0-387-97245-5. Zbl:0706.46003. [1]
• [CC79] P. Cousot, R. Cousot. Constructive Versions of Tarski's Fixed Point Theorems. Pacific Journal of Mathematics, 81(1):43–57, 1979. [1] [2]
• [CLOS97] David A. Cox, John Little, Donal O'Shea. Ideals, varieties, and algorithms - an introduction to computational algebraic geometry and commutative algebra (2. ed.). Undergraduate texts in mathematics. Springer, 1997. ISBN 978-0-387-94680-1. [1]
• [CMP17] Alissa S. Crans, Sujoy Mukherjee, Józef H. Przytycki. On homology of associative shelves. J. Homotopy Relat. Struct., 12(3):741–763, 2017. doi:10.1007/s40062-016-0164-9, MR:3691304, URL: https://doi.org/10.1007/s40062-016-0164-9. [1]
• [DP02] B. A. Davey, H. A. Priestley. Introduction to lattices and order. Second edition. Cambridge University Press, New York, 2002. ISBN 0-521-78451-4. doi:10.1017/CBO9780511809088, MR:1902334, URL: https://doi.org/10.1017/CBO9780511809088. [1] [2] [3]
• [Dav73] Martin Davis. Hilbert's tenth problem is unsolvable. Amer. Math. Monthly, 80:233–269, 1973. doi:10.2307/2318447, MR:317916, URL: https://doi.org/10.2307/2318447. [1] [2]
• [Day72] Brian Day. A reflection theorem for closed categories. J. Pure Appl. Algebra, 2(1):1–11, 1972. doi:10.1016/0022-4049(72)90021-7, URL: https://doi.org/10.1016/0022-4049(72)90021-7. [1]
• [dMKA+15] Leonardo de Moura, Soonho Kong, Jeremy Avigad, Floris van Doorn, Jakob von Raumer. The Lean Theorem Prover (System Description). In Amy P. Felty, Aart Middeldorp, editors, Automated Deduction - CADE-25, 378–388. Cham, 2015. Springer International Publishing.
• [DP89] Valeria De Paiva. The Dialectica categories. Jan 1989. doi:10.1090/conm/092/1003194, URL: https://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-213.pdf. [1] [2]
• [Del75] P. Deligne. Courbes elliptiques: formulaire d'après J. Tate. In Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), 53–73. Lecture Notes in Math., Vol. 476. 1975. MR:0387292. [1]
• [Dem70] Michel Demazure. Exposé XXI, Donées Radicielles. In A. Grothendieck M. Demazure, editor, Séminaire de Géométrie Algébrique du Bois Marie - 1962-64 - Schémas en groupes - (SGA 3) - vol. 3, Structure des Schémas en Groupes Reductifs, volume 153 of Lecture Notes in Mathematics, 85–155. Springer-Verlag, 1970. URL: https://wstein.org/sga/SGA3/Expo21-alpha.pdf. [1] [2]
• [DG70] Michel Demazure, Pierre Gabriel. Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs. Masson & Cie, Éditeur, Paris; North-Holland Publishing Co., Amsterdam, 1970. Avec un appendice ıt Corps de classes local par Michiel Hazewinkel. MR:0302656. [1]
• [Die53] Jean Dieudonné. On semi-simple Lie algebras. Proc. Amer. Math. Soc., 4:931–932, 1953. doi:10.2307/2031832, MR:59262, URL: https://doi.org/10.2307/2031832. [1]
• [DM22] Yaël Dillies, Bhavik Mehta. Formalising Szemerédi’s Regularity Lemma in Lean. In June Andronick, Leonardo de Moura, editors, 13th International Conference on Interactive Theorem Proving (ITP 2022), volume 237 of Leibniz International Proceedings in Informatics (LIPIcs), 9:1–9:19. Dagstuhl, Germany, 2022. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. doi:10.4230/LIPIcs.ITP.2022.9, URL: https://drops.dagstuhl.de/opus/volltexte/2022/16718. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
• [Djo73] D. Ž. Djoković. Epimorphisms of modules which must be isomorphisms. Canad. Math. Bull., 16:513–515, 1973. doi:10.4153/CMB-1973-083-0, MR:346014, URL: https://doi.org/10.4153/CMB-1973-083-0. [1] [2] [3] [4] [5] [6]
• [Dol76] S. W. Dolan. A Proof of Jacobson's Theorem. Canadian Mathematical Bulletin, 19(1):59–61, Mar 1976. doi:10.4153/CMB-1976-007-9.
• [Dol58] Albrecht Dold. Homology of symmetric products and other functors of complexes. Ann. of Math. (2), 68:54–80, 1958. doi:10.2307/1970043, MR:97057. [1] [2] [3]
• [DRS72] Peter Doubilet, Gian-Carlo Rota, Richard Stanley. On the foundations of combinatorial theory. VI. The idea of generating function. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability theory, 267–318. Univ. California Press, Berkeley, CA, 1972. MR:403987. [1]
• [DLM22] Frédéric Dupuis, Robert Y. Lewis, Heather Macbeth. Formalized functional analysis with semilinear maps. 2022. arXiv:2202.05360. [1] [2] [3]
• [Dyc92] Roy Dyckhoff. Contraction-free sequent calculi for intuitionistic logic. Journal of Symbolic Logic, 57(3):795–807, 1992. doi:10.2307/2275431. [1]
• [Ech05] Federico Echenique. A short and constructive proof of Tarski’s fixed-point theorem. International Journal of Game Theory, 33(2):215–218, 2005. doi:10.1007/s001820400192. [1] [2]
• [EW17] Manfred Einsiedler, Thomas Ward. Functional Analysis, Spectral Theory, and Applications. Springer, 2017. doi:10.1007/978-3-319-58540-6. [1]
• [Eis95] David Eisenbud. Commutative algebra. Graduate Texts in Mathematics. Springer, New York, NY, Mar 1995. ISBN 978-0-387-94268-1. doi:10.1007/978-1-4612-5350-1.
• [Ell06] Jesse Elliott. Binomial rings, integer-valued polynomials, and λ-rings. Journal of Pure and Applied Algebra, 207(1):165–185, 2006. doi:10.1016/j.jpaa.2005.09.003. [1] [2]
• [Eng97] Konrad Engel. Sperner theory. Cambridge University Press, 1997. [1] [2]
• [Eng89] Ryszard Engelking. General topology. Second edition. Volume 6 of Sigma Series in Pure Mathematics. Heldermann Verlag, Berlin, 1989. ISBN 3-88538-006-4. Translated from the Polish by the author. MR:1039321. [1]
• [ERS66] P. Erdös, A. Rényi, V. Sós. On a problem of graph theory. Studia Sci. Math., pages 215–235, 1966. URL: https://www.renyi.hu/~p_erdos/1966-06.pdf. [1]
• [Ete81] Nasrollah Etemadi. An elementary proof of the strong law of large numbers. Z. Wahrsch. Verw. Gebiete, 55(1):119–122, 1981. doi:10.1007/BF01013465, MR:606010, URL: https://doi.org/10.1007/BF01013465. [1]
• [EGNO15] Pavel Etingof, Shlomo Gelaki, Dmitri Nikshych, Victor Ostrik. Tensor Categories. American Mathematical Society (AMS), Providence, RI, 2015. ISBN 978-1-4704-3441-0. [1]
• [Fed96] Herbert Federer. Geometric Measure Theory. Classics in Mathematics. Springer-Verlag Berlin Heidelberg, 1996. doi:10.1007/978-3-642-62010-2. [1] [2] [3] [4]
• [FR92] Roger Fenn, Colin Rourke. Racks and links in codimension two. Journal of Knot Theory and its Ramifications, 1(4):343–406, 1992. doi:10.1142/S0218216592000203, MR:1194995. [1]
• [Fie71] David E. Fields. Zero divisors and nilpotent elements in power series rings. Proceedings of the American Mathematical Society, 27(3):427–433, 1971. doi:10.1090/S0002-9939-1971-0271100-6. [1]
• [Fre03] David H. Fremlin. Measure theory. Vol. 4. Torres Fremlin, Colchester, 2003. Topological Measure Spaces. [1] [2] [3]
• [Fre10] David H. Fremlin. Measure theory. Vol. 2. Torres Fremlin, Colchester, 2010. ISBN 0-9538129-2-8. Broad foundations, 2010 edition. [1] [2] [3] [4]
• [Fre57] Jean Frenkel. Cohomologie non abélienne et espaces fibrés. Bull. Soc. Math. France, 85:135–220, 1957. MR:98200, URL: http://www.numdam.org/item?id=BSMF_1957__85__135_0. [1]
• [Fre64] Peter J Freyd. Abelian categories. Harper's Series in Modern Mathematics. Harper & Row New York, 1964. [1]
• [Fri05] Yaakov Friedman. Physical applications of homogeneous balls. With the assistance of Tzvi Scarr. Volume 40. Boston, MA: Birkhäuser, 2005. ISBN 0-8176-3339-1. Zbl:1080.46001. [1]
• [FP90] Rudolf Fritsch, Renzo Piccinini. Cellular Structures in Topology. Cambridge Studies in Advanced Mathematics. Cambridge University Press, 1990. doi:10.1017/CBO9780511983948, URL: https://doi.org/10.1017/CBO9780511983948. [1]
• [Fuc63] L. Fuchs. Partially ordered algebraic systems. Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR:0171864. [1] [2] [3]
• [FH04] William Fulton, Joe Harris. Representation theory: a first course. Springer, 2004. [1]
• [FL94] Zoltán Füredi, Peter A. Loeb. On the best constant for the Besicovitch covering theorem. Proc. Am. Math. Soc., 121(4):1063–1073, 1994. doi:10.2307/2161215, Zbl:0802.28002. [1]
• [FLST20] Basil Fürer, Andreas Lochbihler, Joshua Schneider, Dmitriy Traytel. Quotients of Bounded Natural Functors. In Nicolas Peltier, Viorica Sofronie-Stokkermans, editors, Automated Reasoning - 10th International Joint Conference, IJCAR 2020, Paris, France, July 1-4, 2020, Proceedings, Part II, volume 12167 of Lecture Notes in Computer Science, 58–78. Springer, 2020. doi:10.1007/978-3-030-51054-1_4, URL: https://doi.org/10.1007/978-3-030-51054-1_4.
• [GZ67] P. Gabriel, M. Zisman. Calculus of fractions and homotopy theory. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35. Springer-Verlag New York, Inc., New York, 1967. [1] [2] [3]
• [Gal61] Patrick Gallagher. Approximation by reduced fractions. J. Math. Soc. Japan, 13:342–345, 1961. doi:10.2969/jmsj/01340342, MR:133297, URL: https://doi.org/10.2969/jmsj/01340342.
• [GQ11] J. Gallier, J. Quaintance. Notes on Differential Geometry and Lie Groups. In 2011. URL: https://www.cis.upenn.edu/~cis610/diffgeom-n.pdf. [1]
• [GM] B. Gärtner, J. Matousek. Cone Programming. URL: https://ti.inf.ethz.ch/ew/lehre/ApproxSDP09/notes/conelp.pdf. [1]
• [Ghy87] Étienne Ghys. Groupes d'homéomorphismes du cercle et cohomologie bornée. Contemporary Mathematics, 58(III):81-106, 1987. doi:10.1090/conm/058.3/893858. [1] [2] [3] [4] [5] [6] [7]
• [GO09] Jeremy Gibbons, BRUNO C. d. S. Oliveira. The essence of the Iterator pattern. Journal of Functional Programming, 19(3-4):377–402, Jul 2009. doi:10.1017/S0956796809007291, URL: https://www.cambridge.org/core/product/identifier/S0956796809007291/type/journal_article. [1]
• [GHK+80] Gerhard Gierz, Karl Heinrich Hofmann, Klaus Keimel, Jimmie D. Lawson, Michael W. Mislove, Dana S. Scott. A compendium of continuous lattices. Springer-Verlag, Berlin-New York, 1980. ISBN 3-540-10111-X. MR:614752. [1] [2] [3] [4] [5] [6]
• [Gle58] Andrew M. Gleason. Projective topological spaces. Illinois J. Math., 2:482–489, 1958. MR:121775, URL: http://projecteuclid.org/euclid.ijm/1255454110. [1] [2] [3] [4] [5] [6]
• [GJ09] Paul G. Goerss, John F. Jardine. Simplicial homotopy theory. Modern Birkhäuser Classics. Birkhäuser Verlag, Basel, 2009. ISBN 978-3-0346-0188-7. Reprint of the 1999 edition [MR1711612]. doi:10.1007/978-3-0346-0189-4, MR:2840650. [1] [2] [3] [4] [5] [6]
• [Gor55] Russel A. Gordon. The integrals of Lebesgue, Denjoy, Perron, and Henstock. Volume 4 of Graduate Studies in Mathematics. American Mathematical Society, Providence, R.I, 1955. ISBN 0-8218-3805-9. [1] [2]
• [Gou97] Fernando Q. Gouvêa. $p$-adic numbers. Second edition. Universitext. Springer-Verlag, Berlin, 1997. ISBN 3-540-62911-4. An introduction. doi:10.1007/978-3-642-59058-0, MR:1488696, URL: https://doi.org/10.1007/978-3-642-59058-0. [1] [2] [3] [4] [5]
• [Gra83] R. L. Graham. Applications of the FKG Inequality and Its Relatives, pages 115–131. Springer Berlin Heidelberg, Berlin, Heidelberg, 1983. doi:10.1007/978-3-642-68874-4_6, URL: https://doi.org/10.1007/978-3-642-68874-4_6. [1] [2]
• [Gra11] George Grätzer. Lattice Theory: Foundation. Springer, Basel, 2011. ISBN 978-3-0348-0018-1. doi:10.1007/978-3-0348-0018-1, MR:2768581. [1] [2]
• [Gri69a] Pierre-Antoine Grillet. The Tensor Product of Commutative Semigroups. Transactions of the American Mathematical Society, 138:281–293, 1969. doi:10.1090/S0002-9947-1969-0237688-1. [1]
• [Gri69b] Pierre-Antoine Grillet. The Tensor Product of Semigroups. Transactions of the American Mathematical Society, 138:267–280, 1969. doi:10.1090/S0002-9947-1969-0237687-X.
• [Gri16] D. Grinberg. The Clifford algebra and the Chevalley map- a computational approach (summary version 1). Jun 2016. URL: http://mit.edu/~darij/www/algebra/chevalleys.pdf. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
• [Gui80] René Guitart. Ann. Sci. Math. Québec, 4(2):103–125, 1980. MR:599050. [1]
• [Gun92] Carl A. Gunter. Semantics of Programming Languages: Structures and Techniques. MIT Press, 1992. ISBN 0262570955. [1] [2] [3]
• [GMM] Alena Gusakov, Bhavik Mehta, Kyle A. Miller. Formalizing Hall's Marriage Theorem in Lean. arXiv:2101.00127. [1]
• [Hal35] P. Hall. On Representatives of Subsets. Journal of the London Mathematical Society, s1-10(1):26–30, Jan 1935. doi:10.1112/jlms/s1-10.37.26. [1]
• [Hal50a] Paul R Halmos. Measure theory. Springer-Verlag New York, 1950. ISBN 978-1-4684-9440-2. doi:10.1007/978-1-4684-9440-2. [1] [2] [3]
• [Hal50b] Paul R Halmos. Measure theory. Volume 18. Springer, 1950. ISBN 0-387-90088-8.
• [Hal66] James D. Halpern. Bases in vector spaces and the axiom of choice. Proc. Amer. Math. Soc., 17:670–673, 1966. doi:10.2307/2035388, MR:194340. [1]
• [HvD19] Jesse Michael Han, Floris van Doorn. A Formalization of Forcing and the Unprovability of the Continuum Hypothesis. In John Harrison, John O'Leary, Andrew Tolmach, editors, 10th International Conference on Interactive Theorem Proving (ITP 2019), volume 141 of Leibniz International Proceedings in Informatics (LIPIcs), 19:1–19:19. Dagstuhl, Germany, 2019. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik. doi:10.4230/LIPIcs.ITP.2019.19, URL: http://drops.dagstuhl.de/opus/volltexte/2019/11074. [1] [2] [3] [4]
• [HvD20] Jesse Michael Han, Floris van Doorn. A formal proof of the independence of the continuum hypothesis. In Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs. ACM, Jan 2020. doi:10.1145/3372885.3373826, URL: https://doi.org/10.1145/3372885.3373826. [1] [2] [3] [4]
• [HOS84] Harald Hanche-Olsen, Erling Størmer. Jordan operator algebras. Volume 21. Pitman, Boston, MA, 1984. Zbl:0561.46031. [1] [2]
• [HWHBS08] GH Hardy, EM Wright, Roger Heath-Brown, Joseph Silverman. An Introduction to the Theory of Numbers. Oxford University Press, 2008. [1] [2] [3]
• [HWW93] Peter Harmand, Dirk Werner, Wend Werner. $M$-ideals in Banach spaces and Banach algebras. Volume 1547. Berlin: Springer-Verlag, 1993. ISBN 3-540-56814-X. doi:10.1007/BFb0084355, Zbl:0789.46011. [1]
• [Har67] Robin Hartshorne. Local cohomology. Lecture Notes in Mathematics, No. 41. Springer-Verlag, Berlin-New York, 1967. A seminar given by A. Grothendieck, Harvard University, Fall, 1961. MR:0224620. [1]
• [Har77] Robin Hartshorne. Algebraic geometry. Springer-Verlag, New York-Heidelberg, 1977. ISBN 0-387-90244-9. Graduate Texts in Mathematics, No. 52. MR:0463157. [1]
• [Haz09] Michiel Hazewinkel. Witt vectors. Part 1. Handbook of Algebra, pages 319–472, 2009. doi:10.1016/s1570-7954(08)00207-6, URL: http://dx.doi.org/10.1016/S1570-7954(08)00207-6. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
• [Hib75] Jean-Jacques Hiblot. Des anneaux euclidiens dont le plus petit algorithme n'est pas à valeurs finies. C. R. Acad. Sci. Paris Sér. A-B, 281(12):Ai, A411–A414, 1975. MR:399081. [1]
• [Hig52] Graham Higman. Ordering by Divisibility in Abstract Algebras. Proceedings of the London Mathematical Society, s3-2(1):326-336, 1952. doi:10.1112/plms/s3-2.1.326. [1]
• [HS00] Marc Hindry, Joseph H. Silverman. Diophantine geometry. Volume 201 of Graduate Texts in Mathematics. Springer-Verlag, New York, 2000. An introduction. [1]
• [Hoc] Mel Hochster. Local cohomology. URL: https://dept.math.lsa.umich.edu/~hochster/615W11/loc.pdf. [1]
• [Hod97] Wilfrid Hodges. A Shorter Model Theory. Cambridge University Press, USA, 1997. ISBN 0521587131. [1]
• [Hof79] Douglas R Hofstadter. Gödel, Escher, Bach: an eternal golden braid. Penguin books. Basic Books, New York, NY, 1979. [1]
• [Hov01] Mark Hovey. Model category structures on chain complexes of sheaves. Trans. Amer. Math. Soc., 353(6):2441–2457, 2001. doi:10.1090/S0002-9947-01-02721-0, MR:1814077, URL: https://doi.org/10.1090/S0002-9947-01-02721-0. [1]
• [How] Peter Howard. Second Order Elliptic PDE: The Lax-Milgram Theorem. URL: https://www.math.tamu.edu/~phoward/m612/s20/elliptic2.pdf. [1]
• [Hua82] Loo-Keng Hua. Introduction to Number Theory. Springer, 1982. [1]
• [HW91] John H. Hubbard, Beverly H. West. Differential Equations: A Dynamical Systems Approach. Volume 5. Springer, 1991. ISBN 978-1-4612-8693-6. doi:10.1007/978-1-4612-4192-8. [1]
• [Hun02] Craig Huneke. The Friendship Theorem. The American Mathematical Monthly, 109(2):192–194, 2002. doi:10.1080/00029890.2002.11919853, URL: https://doi.org/10.1080/00029890.2002.11919853. [1]
• [Ior03] Radu Iordănescu. Jordan structures in geometry and physics. With an appendix on Jordan structures in analysis. Bucharest: Editura Academiei Române, 2003. ISBN 973-27-0956-1. Zbl:1073.17014. [1]
• [IR90] Kenneth Ireland, Michael Rosen. A classical introduction to modern number theory. Second edition. Volume 84 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1990. ISBN 0-387-97329-X. doi:10.1007/978-1-4757-2103-4, URL: https://doi.org/10.1007/978-1-4757-2103-4. [1] [2]
• [Isa80] I. M. Isaacs. Roots of Polynomials in Algebraic Extensions of Fields. The American Mathematical Monthly, 87(7):543–544, 1980. doi:10.1080/00029890.1980.11995085, URL: https://doi.org/10.1080/00029890.1980.11995085. [1] [2] [3]
• [Ive06] Birger Iversen. Generic Local Structure of the Morphisms in Commutative Algebra. Volume 310 of Lecture Notes in Mathematics. Springer Berlin, Heidelberg, 2006. ISBN 978-3-540-06137-3. doi:10.1007/BFb0060790. [1] [2] [3] [4] [5] [6]
• [ILL+07] Srikanth B. Iyengar, Graham J. Leuschke, Anton Leykin, Claudia Miller, Ezra Miller, Anurag K. Singh, Uli Walther. Twenty-four hours of local cohomology. Volume 87 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 2007. ISBN 978-0-8218-4126-6. doi:10.1090/gsm/087, URL: https://doi-org.www2.lib.ku.edu/10.1090/gsm/087.
• [IKR16] Zur Izhakian, Manfred Knebusch, Louis Rowen. Supertropical quadratic forms I. Journal of Pure and Applied Algebra, 220(1):61-93, 2016. doi:10.1016/j.jpaa.2015.05.043, URL: https://www.sciencedirect.com/science/article/pii/S0022404915001589. [1]
• [Jac56] Nathan Jacobson. Structure of rings. Volume 37 of Colloq. Publ., Am. Math. Soc. American Mathematical Society (AMS), Providence, RI, 1956. Zbl:0073.02002. [1]
• [Jac74] Nathan Jacobson. Basic algebra. I. W. H. Freeman and Co., San Francisco, CA, 1974. MR:356989. [1]
• [Jac89] Nathan Jacobson. Basic algebra. II. Second edition. W. H. Freeman and Company, New York, 1989. ISBN 0-7167-1933-9. MR:1009787.
• [Jam99] Ioan James. Topologies and uniformities. Springer Undergraduate Mathematics Series. Springer-Verlag London, Ltd., London, 1999. ISBN 1-85233-061-9. Revised version of ıt Topological and uniform spaces [Springer, New York, 1987; MR0884154 (89b:54001)]. doi:10.1007/978-1-4471-3994-2, MR:1687407, URL: https://doi.org/10.1007/978-1-4471-3994-2. [1] [2]
• [Joh02] Peter Johnstone. Sketches of an Elephant – A Topos Theory Compendium. Oxford University Press, 2002. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]
• [JvN35] P. Jordan, J. von Neumann. On inner products in linear, metric spaces. Ann. Math., 36(3):719-723, Jul 1935. doi:10.2307/1968653, URL: http://www.mathematik.uni-muenchen.de/~michel/jordan-von_neumann_-_parallelogram_identity.pdf. [1]
• [Joy77] André Joyal. Remarques sur la théorie des jeux à deux personnes. Gazette des Sciences Mathematiques du Québec, 1(4):46–52, 1977. (English translation at https://bosker.files.wordpress.com/2010/12/joyal-games.pdf).
• [JS86] André Joyal, Ross H. Street. Braided monoidal categories. 1986. Mathematics Reports 860081, Macquarie University. URL: http://maths.mq.edu.au/~street/JS1.pdf.
• [Joy82] David Joyce. A classifying invariant of knots, the knot quandle. Journal of Pure and Applied Algebra, 23(1):37–65, Jan 1982. doi:10.1016/0022-4049(82)90077-9. [1] [2]
• [JW22] Adolf P Juškevič, Eduard Winter. Leonhard Euler und Christian Goldbach: Briefwechsel 1729–1764. Walter de Gruyter GmbH & Co KG, 2022. [1]
• [KM08] Bruno Kahn, Georges Maltsiniotis. Structures de dérivabilité. Adv. Math., 218(4):1286–1318, 2008. doi:10.1016/j.aim.2008.03.010, MR:2419385, URL: https://doi.org/10.1016/j.aim.2008.03.010. [1] [2] [3] [4] [5] [6] [7] [8] [9]
• [Kal17] Olav Kallenberg. Random Measures, Theory and Applications. Volume 77 of Probability Theory and Stochastic Modelling. Springer, 2017. doi:10.1007/978-3-319-41598-7, URL: https://doi.org/10.1007/978-3-319-41598-7. [1]
• [Kal21] Olav Kallenberg. Foundations of modern probability. Third Edition. Volume 99 of Probability Theory and Stochastic Modelling. Springer Nature Switzerland, 2021. ISBN 978-3-030-61870-4; 978-3-030-61871-1. doi:10.1007/978-3-030-61871-1, URL: https://doi.org/10.1007/978-3-030-61871-1. [1] [2] [3]
• [Kar04] Georg Karner. Continuous monoids and semirings. Theor. Comput. Sci., 318(3):355–372, 2004. doi:10.1016/j.tcs.2004.01.020, Zbl:1068.68079. [1]
• [KS06] Masaki Kashiwara, Pierre Schapira. Categories and Sheaves. Springer Berlin Heidelberg, 2006. doi:10.1007/3-540-27950-4, URL: https://doi.org/10.1007/3-540-27950-4. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
• [Kas95] Christian Kassel. Quantum groups. Volume 155 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. ISBN 0-387-94370-6. doi:10.1007/978-1-4612-0783-2, MR:1321145, URL: https://doi.org/10.1007/978-1-4612-0783-2. [1] [2]
• [KM85] Nicholas M. Katz, Barry Mazur. Arithmetic moduli of elliptic curves. Volume 108 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 1985. ISBN 0-691-08349-5; 0-691-08352-5. doi:10.1515/9781400881710, MR:772569, URL: https://doi.org/10.1515/9781400881710. [1]
• [Kay91] Richard Kaye. Models of Peano Arithmetic. Clarendon Press, 1991. [1]
• [Kec95] Alexander S. Kechris. Classical descriptive set theory. Volume 156 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. ISBN 0-387-94374-9. doi:10.1007/978-1-4612-4190-4, MR:1321597, URL: https://doi.org/10.1007/978-1-4612-4190-4. [1] [2] [3]
• [KV53] J. L. Kelley, R. L. Vaught. The positive cone in Banach algebras. Trans. Am. Math. Soc., 74:44–55, 1953. doi:10.2307/1990847. [1] [2]
• [Kle79] Steven Lawrence Kleiman. Misconceptions about $K_X$. Enseign. Math. (2), 25(3-4):203–206, 1979. URL: http://dx.doi.org/10.5169/seals-50379. [1]
• [Kle66] D. J. Kleitman. Families of non-disjoint subsets. J. Comb. Theory, 1:153–155, 1966. doi:10.1016/S0021-9800(66)80012-1, Zbl:0141.00801. [1] [2] [3]
• [KM20] Dimitris Koukoulopoulos, James Maynard. On the Duffin-Schaeffer conjecture. Ann. of Math. (2), 192(1):251–307, 2020. doi:10.4007/annals.2020.192.1.5, MR:4125453, URL: https://doi.org/10.4007/annals.2020.192.1.5.
• [Koz94] D. Kozen. A Completeness Theorem for Kleene Algebras and the Algebra of Regular Events. Information and Computation, 110(2):366-390, 1994. doi:10.1006/inco.1994.1037, URL: https://www.sciencedirect.com/science/article/pii/S0890540184710376. [1]
• [KRY09] Joseph P. S. Kung, Gian-Carlo Rota, Catherine H. Yan. Combinatorics: the Rota way. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 2009. ISBN 978-0-521-73794-4. doi:10.1017/CBO9780511803895, MR:2483561, URL: https://doi.org/10.1017/CBO9780511803895. [1]
• [LS04] S. Lack, P. Sobociński. Adhesive categories. In Foundations of Software Science and Computation Structures, FoSSaCS '04, volume 2987 of LNCS, 273–288. Springer, 2004. URL: https://www.ioc.ee/~pawel/papers/adhesive.pdf. [1] [2]
• [Lam99] T. Y. Lam. Lectures on Modules and Rings. Graduate Texts in Mathematics. Springer New York, NY, 1999. doi:10.1007/978-1-4612-0525-8. [1] [2]
• [Lam84] T.Y. Lam. An introduction to real algebra. Rocky Mountain Journal of Mathematics, 14(4):767 – 814, 1984. doi:10.1216/RMJ-1984-14-4-767, URL: https://doi.org/10.1216/RMJ-1984-14-4-767.
• [Lan02] Serge Lang. Algebra. Third edition. Graduate Texts in Mathematics. Springer New York, NY, 2002. ISBN 978-0-387-95385-4. doi:10.1007/978-1-4613-0041-0. [1]
• [Laz73] Michel Lazarus. Les familles libres maximales d'un module ont-elles le meme cardinal? Pub. Sem. Math. Rennes, 4:1–12, 1973. URL: http://www.numdam.org/article/PSMIR_1973___4_A4_0.pdf. [1]
• [Lee12] John Lee. Introduction to Smooth Manifolds. 2nd ed. 2013 edition. Springer New York, 2012. URL: https://doi.org/10.1007/978-1-4419-9982-5. [1] [2] [3] [4] [5]
• [Len] Hendrik Willem Lenstra. Galois theory for schemes. URL: https://websites.math.leidenuniv.nl/algebra/GSchemes.pdf. [1] [2] [3]
• [Lew19] Robert Y. Lewis. A Formal Proof of Hensel's Lemma over the $p$-adic Integers. In Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2019, 15–26. New York, NY, USA, 2019. ACM. doi:10.1145/3293880.3294089, URL: http://doi.acm.org/10.1145/3293880.3294089. [1] [2] [3] [4] [5] [6]
• [LMT93] R. Lidl, G. L. Mullen, G. Turnwald. Dickson polynomials. Volume 65 of Pitman Monographs and Surveys in Pure and Applied Mathematics. Longman Scientific & Technical, Harlow; copublished in the United States with John Wiley & Sons, Inc., New York, 1993. ISBN 0-582-09119-5. MR:1237403. [1]
• [Lur18] Jacob Lurie. Spectral Algebraic Geometry. last updated 2018. URL: https://www.math.ias.edu/~lurie/papers/SAG-rootfile.pdf. [1]
• [MLM92] Saunders MacLane, Ieke Moerdijk. Sheaves in geometry and logic: A first introduction to topos theory. Springer Science & Business Media, 1992. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43]
• [Man63] Ju. I. Manin. Theory of commutative formal groups over fields of finite characteristic. Uspehi Mat. Nauk, 18(6 (114)):3–90, 1963. MR:0157972. [1]
• [MS77] Daniel A Marcus, Emanuele Sacco. Number fields. Volume 2. Springer, 1977. [1] [2] [3] [4] [5] [6] [7] [8]
• [Mar76] George Markowsky. Chain-complete posets and directed sets with applications. Algebra Universalis, 6(1):53-68, Dec 1976. doi:10.1007/bf02485815. [1]
• [mC20] The mathlib Community. The Lean Mathematical Library. In Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP 2020, 367-381. New York, NY, USA, 2020. Association for Computing Machinery. doi:10.1145/3372885.3373824, URL: https://doi.org/10.1145/3372885.3373824.
• [Mat95] Pertti Mattila. Geometry of sets and measures in Euclidean spaces. Volume 44 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1995. ISBN 0-521-46576-1; 0-521-65595-1. Fractals and rectifiability. doi:10.1017/CBO9780511623813, URL: https://doi.org/10.1017/CBO9780511623813.
• [McB96] Conor McBride. Inverting inductively defined relations in LEGO. In International Workshop on Types for Proofs and Programs, 236–253. Springer, 1996.
• [McC04] Kevin McCrimmon. A taste of Jordan algebras. New York, NY: Springer, 2004. ISBN 0-387-95447-3. doi:10.1007/b97489, Zbl:1044.17001. [1] [2] [3]
• [Mel11] Sergey A. Melikhov. Metrizable uniform spaces. 2011. arXiv:1106.3249. [1]
• [MN91] Peter Meyer-Nieberg. Banach lattices. Universitext. Springer-Verlag, Berlin, 1991. ISBN 3-540-54201-9. doi:10.1007/978-3-642-76724-1, MR:1128093, URL: https://doi.org/10.1007/978-3-642-76724-1. [1]
• [Mir06] F. Miraglia. An Introduction to Partially Ordered Structures and Sheaves. Contemporary logic. Polimetrica, 2006. ISBN 9788876990359. [1]
• [Mot49] Th. Motzkin. The Euclidean algorithm. Bull. Amer. Math. Soc., 55:1142–1146, 1949. doi:10.1090/S0002-9904-1949-09344-8, MR:32592, URL: https://doi.org/10.1090/S0002-9904-1949-09344-8. [1]
• [Mul86] Christopher J. Mulvey. &. Suppl. Rend. Circ. Mat. Palermo (2), 12:99–104, 1986. Zbl:0633.46065. [1]
• [Nag78] Masayoshi Nagata. On Euclid algorithm. In C. P. Ramanujam—a tribute, volume 8 of Tata Inst. Fund. Res. Studies in Math., pages 175–186. Springer, Berlin-New York, 1978. MR:541021. [1]
• [Nao15] Assaf Naor. Metric Embeddings and Lipschitz Extensions. 2015. URL: https://web.math.princeton.edu/~naor/homepage%20files/embeddings_extensions.pdf. [1] [2]
• [NW63] C. St. J. A. Nash-Williams. On well-quasi-ordering finite trees. Mathematical Proceedings of the Cambridge Philosophical Society, 59(4):833–835, 1963. doi:10.1017/S0305004100003844. [1]
• [Neu99] J. Neukirch. Algebraic number theory. Volume 322 of Fundamental Principles of Mathematical Sciences. Springer-Verlag, Berlin, 1999. ISBN 3-540-65399-6. Translated from the 1992 German original and with a note by Norbert Schappacher, With a foreword by G. Harder. doi:10.1007/978-3-662-03983-0. [1] [2] [3] [4] [5] [6] [7] [8]
• [Neu54] B. H. Neumann. Groups Covered By Permutable Subsets. Journal of the London Mathematical Society, s1-29(2):236–248, Apr 1954. doi:10.1112/jlms/s1-29.2.236. [1]
• [Okn91] Jan Okniński. Semigroup algebras. Marcel Dekker, 1991. [1]
• [Oro18] Greg Orosi. A simple derivation of Faulhaber's formula. Appl. Math. E-Notes, 18:124–126, 2018. Zbl:1411.41023. [1]
• [Orz71] Morris Orzech. Onto endomorphisms are isomorphisms. Amer. Math. Monthly, 78:357–362, 1971. doi:10.2307/2316897, MR:280475, URL: https://doi.org/10.2307/2316897. [1] [2] [3] [4] [5] [6]
• [Oxl11] James Oxley. Matroid Theory. Oxford University Press, Feb 2011. ISBN 9780198566946. doi:10.1093/acprof:oso/9780198566946.001.0001, URL: https://doi.org/10.1093/acprof:oso/9780198566946.001.0001. [1] [2]
• [Per69] Hazel Perfect. Independence Spaces and Combinatorial Problems. Proceedings of the London Mathematical Society, s3-19(1):17-30, 1969. doi:10.1112/plms/s3-19.1.17, URL: https://londmathsoc.onlinelibrary.wiley.com/doi/pdf/10.1112/plms/s3-19.1.17, URL: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/plms/s3-19.1.17. [1] [2]
• [Pet14] G. Petridis. The Plünnecke-Ruzsa inequality: an overview. In Combinatorial and additive number theory. Selected papers based on the presentations at the conferences CANT 2011 and 2012, New York, NY, USA, May 2011 and May 2012, pages 229–241. New York, NY: Springer, 2014. doi:10.1007/978-1-4939-1601-6_16, Zbl:1371.11029. [1]
• [Phi40] Ralph S. Phillips. Integration in a convex linear topological space. Trans. Amer. Math. Soc., 47:114–145, 1940. doi:10.2307/1990004, MR:2707, URL: https://doi.org/10.2307/1990004. [1]
• [PP11] Jorge Picado, Aleš Pultr. Frames and Locales: topology without points. Birkhäuser Basel, 2011. ISBN 9783034801539. doi:10.1007/978-3-0348-0154-6. [1]
• [Pon20] Lionel Ponton. Roots of Chebyshev polynomials: a purely algebraic approach. 2020. arXiv:2008.03575. [1]
• [Pos17] Jürgen Pöschel. On the Siegel-Sternberg linearization theorem. 2017. arXiv:1702.03691. [1]
• [Pri70] Robert W. Prielipp. PERFECT NUMBERS, ABUNDANT NUMBERS, AND DEFICIENT NUMBERS. The Mathematics Teacher, 63:692–696, 1970. URL: http://www.jstor.org/stable/27958492. [1]
• [Rib71] Paulo Ribenboim. Épimorphismes de modules qui sont nécessairement des isomorphismes. In Séminaire P. Dubreil, M.-L. Dubreil-Jacotin, L. Lesieur et C. Pisot (24ème année: 1970/71), Algèbre et théorie des nombres, Fasc. 2, pages Exp. No. 19, 5. Éd. Acad. RS Roumanie, Bucharest, 1971. MR:393128. [1] [2] [3] [4]
• [Rie17] Emily Riehl. Category theory in context. Dover Publications, 2017. ISBN 048680903X. URL: http://www.math.jhu.edu/~eriehl/context.pdf. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
• [Rob63] Norbert Roby. Lois polynomes et lois formelles en théorie des modules. Annales scientifiques de l'École Normale Supérieure, 80(3):213–348, 1963. doi:10.24033/asens.1124. [1]
• [Rob65] Norbert Roby. Les Algèbres à Puissances Divisées. Bulletin des Sciences Mathématiques. Deuxième Série, 89:75–91, 1965. [1] [2]
• [Ros72] Maxwell Rosenlicht. Integration in finite terms. Am. Math. Mon., 79:963–972, 1972. doi:10.2307/2318066, Zbl:0249.12106. [1]
• [Rud69] Mary Ellen Rudin. A new proof that metric spaces are paracompact. Proc. Amer. Math. Soc., 20:603, 1969. doi:10.1090/S0002-9939-1969-0236876-3, MR:0236876. [1] [2]
• [Rud87] Walter Rudin. Real and Complex Analysis. Third Edition. McGraw-Hill Book Company, 1987. ISBN 0-07-100276-6. [1] [2]
• [Ruz09] Imre Ruzsa. Sumsets and structure. Combinatorial Number Theory and Additive Group Theory, Jan 2009. [1]
• [Sal18] David Salwinski. Euler's sine product formula: an elementary proof. College Math. J., 49(2):126–135, 2018. doi:10.1080/07468342.2018.1419703, MR:3766700. [1]
• [Sam67] Pierre Samuel. Théorie algébrique des nombres. Hermann, Paris, 1967. MR:0215808. [1] [2] [3]
• [Sch66] H.H. Schaefer. Topological Vector Spaces. Graduate Texts in Mathematics. Macmillan, 1966. [1] [2] [3] [4] [5] [6] [7]
• [SS] Dierk Schleicher, Michael Stoll. An introduction to Conway's games and numbers. URL: http://www.cs.cmu.edu/afs/cs/academic/class/15859-s05/www/lecture-notes/comb-games-notes.pdf.
• [Sch11] Peter Scholze. Perfectoid spaces. 2011. arXiv:1111.4914. [1]
• [Sch19] Peter Scholze. Lectures on Condensed Mathematics. 2019. URL: https://www.math.uni-bonn.de/people/scholze/Condensed.pdf. [1] [2] [3] [4] [5] [6] [7] [8] [9]
• [Sel67] G. B. Seligman. Modular Lie algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 40. Springer-Verlag New York, Inc., New York, 1967. MR:0245627.
• [Ser51] Jean-Pierre Serre. Homologie singulière des espaces fibrés. Applications. Ann. of Math. (2), 54:425–505, 1951. doi:10.2307/1969485, MR:0045386. [1] [2] [3] [4]
• [Ser87] Jean-Pierre Serre. Complex semisimple Lie algebras. Springer-Verlag, New York, 1987. ISBN 0-387-96569-6. Translated from the French by G. A. Jones. doi:10.1007/978-1-4757-3910-7, MR:914496, URL: https://doi.org/10.1007/978-1-4757-3910-7.
• [Sil09] Joseph Silverman. The Arithmetic of Elliptic Curves. Graduate Texts in Mathematics. Springer New York, NY, 2009. [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13]
• [Sim11] Barry Simon. Convexity: An Analytic Viewpoint. Cambridge Tracts in Mathematics. Cambridge University Press, 2011. doi:10.1017/CBO9780511910135. [1] [2] [3] [4]
• [Sko06] Zoran Škoda. Noncommutative localization in noncommutative geometry. London Math. Soc. Lecture Note Series, 330:220–313, 2006. URL: https://doi.org/10.48550/arXiv.math/0403276. [1] [2]
• [Soa87] Robert I. Soare. Recursively enumerable sets and degrees. Perspectives in Mathematical Logic. Springer-Verlag, Berlin, 1987. ISBN 3-540-15299-7. A study of computable functions and computably generated sets. doi:10.1007/978-3-662-02460-7, MR:882921. [1]
• [SOD97] Eugene Spiegel, Christopher J. O'Donnell. Incidence algebras. Volume 206 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, Inc., New York, 1997. ISBN 0-8247-0036-8. MR:1445562. [1]
• [Sta12] Richard P. Stanley. Enumerative combinatorics. Cambridge Univ. Press, 2012. [1] [2]
• [Ste09] Manfred Stern. Semimodular lattices. Theory and applications. Reprint of the 1999 hardback ed. Cambridge: Cambridge University Press, 2009. ISBN 978-0-521-11884-2. Zbl:1175.06002. [1]
• [Sto79] A. H. Stone. Inverse limits of compact spaces. General Topology Appl., 10(2):203–211, 1979. doi:10.1016/0016-660x(79)90008-4, MR:527845. [1]
• [Sto35] M. H. Stone. Postulates for Boolean Algebras and Generalized Boolean Algebras. American Journal of Mathematics, 1935. doi:10.2307/2371008. [1] [2]
• [Sto38] M. H. Stone. Topological representations of distributive lattices and Brouwerian logics. Časopis pro pěstování matematiky a fysiky, 1938. URL: http://dml.cz/dmlcz/124080.
• [Str80] Andrzej Strojnowski. A note on u.p. groups. Communications in Algebra, 8(3):231-234, 1980. doi:10.1080/00927878008822456. [1]
• [Tao10] Terence Tao. An Epsilon of Room, I: Real Analysis: Pages from Year Three of a Mathematical Blog. American Mathematical Society, 2010. URL: https://terrytao.files.wordpress.com/2010/02/epsilon.pdf. [1]
• [TV06] Terence Tao, Van H. Vu. Additive combinatorics. Volume 105 of Camb. Stud. Adv. Math. Cambridge: Cambridge University Press, 2006. ISBN 0-521-85386-9. Zbl:1127.11002. [1]
• [TW95] Richard Taylor, Andrew Wiles. Ring-theoretic properties of certain Hecke algebras. Ann. of Math. (2), 141(3):553–572, 1995. doi:10.2307/2118560, MR:1333036, URL: https://doi.org/10.2307/2118560. [1]
• [TZ12] Katrin Tent, Martin Ziegler. A Course in Model Theory. Lecture Notes in Logic. Cambridge University Press, 2012. doi:10.1017/CBO9781139015417. [1]
• [Toc] Shigenori Tochiori. Considering the Proof of "There is a Prime between n and 2n". URL: https://www.chart.co.jp/subject/sugaku/suken_tsushin/76/76-8.pdf. [1]
• [Upm87] Harald Upmeier. Jordan algebras in analysis, operator theory, and quantum mechanics. Volume 67. Providence, RI: American Mathematical Society (AMS), 1987. ISBN 0-8218-0717-X. Zbl:0608.17013. [1]
• [Vai03] Jussi Väisälä. A Proof of the Mazur-Ulam Theorem. The American Mathematical Monthly, 110(7):633-635, 2003. doi:10.2307/3647749, URL: https://www.jstor.org/stable/3647749. [1]
• [Vak] Ravi Vakil. The Rising Sea: Foundations Of Algebraic Geometry Notes. URL: https://math.stanford.edu/~vakil/216blog/. [1] [2] [3]
• [vdH01] Joris van der Hoeven. Operators on generalized power series. Illinois Journal of Mathematics, 45, Dec 2001. doi:10.1215/ijm/1258138061. [1] [2] [3] [4] [5] [6]
• [vdW48] B. L. van der Waerden. Free products of groups. Amer. J. Math., 70:527–528, 1948. doi:10.2307/2372196, MR:25465, URL: https://doi.org/10.2307/2372196. [1]
• [Ver96] Jean-Louis Verdier. Des catégories dérivées des catégories abéliennes. Number 239. 1996. With a preface by Luc Illusie, Edited and with a note by Georges Maltsiniotis. MR:1453167. [1] [2] [3] [4] [5] [6] [7] [8] [9]
• [Vic89] Steven Vickers. Topology via Logic. University of Cambridge, 1989. ISBN 0-521-57651-2. [1]
• [Vis04] Angelo Vistoli. Notes on Grothendieck topologies, fibered categories and descent theory. Preprint, arXiv:math/0412512 [math.AG] (2004), 2004. URL: https://arxiv.org/abs/math/0412512.
• [Wal18] H.S. Wall. Analytic Theory of Continued Fractions. Dover Books on Mathematics. Dover Publications, 2018. ISBN 9780486830445. [1] [2]
• [Was97] Lawrence C. Washington. Introduction to cyclotomic fields. Second edition. Volume 83 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1997. [1]
• [Was04] Larry Wasserman. All Of Statistics: A Concise Course in Statistical Inference. Springer, 2004.
• [Wed19] Torsten Wedhorn. Adic Spaces. 2019. arXiv:1910.05934. [1] [2] [3] [4]
• [Wei80] Joachim Weidmann. Linear operators in Hilbert spaces. Volume 68 of Graduate Texts in Mathematics. Springer, 1980. ISBN 0-387-90427-1. Translated from the German by Joseph Szücs. [1] [2]
• [WG] Emo Welzl, Bernd Gärtner. Cone Programming. URL: https://ti.inf.ethz.ch/ew/lehre/ApproxSDP09/notes/conelp.pdf. [1]
• [Wie64] Helmut Wielandt. Finite Permutation Groups. Academic Paperbacks. Academic Press, New York, 1964. ISBN 978-0-12-749650-4. [1]
• [Wil95] Andrew Wiles. Modular elliptic curves and Fermat's last theorem. Ann. of Math. (2), 141(3):443–551, 1995. doi:10.2307/2118559, MR:1333035, URL: https://doi.org/10.2307/2118559. [1]
• [Wil04] Stephen Willard. General topology. Reprint of the 1970 original edition. Mineola, NY: Dover Publications, 2004. ISBN 0-486-43479-6. Zbl:1052.54001. [1] [2]
• [Zaa66] A. C. Zaanen. Lectures on "Riesz Spaces". Technical Report EUR 3140.e, Euratom, 1966. [1] [2]
• [Zag90] Don Zagier. A One-Sentence Proof That Every Prime $p\equiv 1(\mod 4)$ Is a Sum of Two Squares. The American Mathematical Monthly, 97(2):144, 1990. doi:10.2307/2323918, URL: https://doi.org/10.2307/2323918.
• [Zei84] Doron Zeilberger. A combinatorial proof of Newton's identities. Discrete Mathematics, 49(3):319, 1984. doi:10.1016/0012-365X(84)90171-7, Zbl:0535.05010, URL: https://doi.org/10.1016/0012-365X(84)90171-7. [1]
• [Zor37] Max Zorn. On a theorem of Engel. Bull. Amer. Math. Soc., 43(6):401–404, 1937. doi:10.1090/S0002-9904-1937-06565-7, MR:1563550, URL: https://doi.org/10.1090/S0002-9904-1937-06565-7.
• [Zwi03] Daniel Zwillinger. CRC standard mathematical tables and formulae. 31st ed. chapman and hall/CRC, 2003.