Zulip Chat Archive

Stream: maths

Topic: axiom of unique choice


view this post on Zulip Kenny Lau (Apr 17 2018 at 04:50):

Is the axiom of unique choice strictly weaker than the axiom of choice? From what I know, ZF has axiom of unique choice

view this post on Zulip Mario Carneiro (Apr 17 2018 at 04:58):

Yes, as you observe

view this post on Zulip Kevin Buzzard (Apr 17 2018 at 07:38):

There are models of ZF in which choice fails, and I am not entirely sure what the axiom of unique choice is, but the definition of a function in set theory is a collection of ordered pairs (a,b) such that for every a there's at most one b, and I would imagine that for some reasonable interpretation of the axiom of unique choice, you can use the axiom of replacement to build such a set.

view this post on Zulip Kenny Lau (Apr 17 2018 at 07:39):

unique choice := nonempty X -> subsingleton X -> X

view this post on Zulip Mario Carneiro (Apr 17 2018 at 07:40):

The axiom of unique choice is true in the standard set theoretic model of type theory without the axiom of choice

view this post on Zulip Mario Carneiro (Apr 17 2018 at 07:41):

although I recall a result that a Tarski universe is well-orderable, so the universes axiom might also imply full choice

view this post on Zulip Mario Carneiro (Apr 17 2018 at 07:45):

relevant: https://cs.nyu.edu/pipermail/fom/2008-March/012783.html


Last updated: May 09 2021 at 10:11 UTC