It is shown that in ZF Martin's $ \aleph_{0}^{}$-axiom together with the axiom of countable choice for finite sets imply that arbitrary powers 2^X of a 2-point discrete space are Baire; and that the latter property implies the following: (a) the axiom of countable choice for finite sets, (b) power sets of infinite sets are Dedekind-infinite, (c) there are no amorphous sets, and (d) weak forms of the Kinna-Wagner principle.