Set Theory/The axiom of choice

Definition (axiom of countable finite choice):

The axiom of countable finite choice states that whenever is a countable family of non-empty sets, then there exists a sequence such that .


  1. Prove that Zorn's lemma is equivalent to Tukey's lemma which states that whenever   is a set and   has the property that   if and only if   for all finite sets  , then for all   there exists a maximal   among all sets in   that contain   (where we consider   to be ordered by inclusion).