Zulip Chat Archive

Stream: maths

Topic: Terence Tao's proof of Hilbert's Nullstellensatz


view this post on Zulip Kenny Lau (May 15 2018 at 20:42):

In this post by Terence Tao, he proved Hilbert's Nullstellensatz in a more elementary and computational manner. My question is: how constructive is this proof?

view this post on Zulip Mario Carneiro (May 15 2018 at 20:51):

I believe it is constructive, but note:

in an explicitly computable fashion (using only the operations of addition, subtraction, multiplication, division, and branching on whether a given field element is zero or non-zero)

Of course "branching on whether a given field element is zero or non-zero" means he needs decidable equality for the base field, so the most obvious application, for the base field C, doesn't work without a bit of nonconstructive magic. However there are decidable algebraically closed fields; the algebraic numbers have decidable equality and are algebraically closed so would probably work with the proof.


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