# Zulip Chat Archive

## Stream: maths

### Topic: axiom of unique choice

#### 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

#### Mario Carneiro (Apr 17 2018 at 04:58):

Yes, as you observe

#### 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.

#### Kenny Lau (Apr 17 2018 at 07:39):

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

#### 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

#### 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

#### 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