Axiom of Choice: Finite Character & Maximal Sets

[quasar987]

There is an axiom/lemma from Teichmilles & Tukey that is equivalent to the axiom of choice. It reads,

Every family of sets F that is of finite character (http://en.wikipedia.org/wiki/Finite_character) possesses a maximal element.

I just want to confirm that here, "maximal set" means a set that is itself contained in no greater set?

 

[morphism]

Yup.

 

[Coin]

Hooray for the axiom of choice!