We study the reverse mathematics of countable analogues of several maximality
principles that are equivalent to the axiom of choice in set theory. Among
these are the principle asserting that every family of sets has a
β-maximal subfamily with the finite intersection property and the
principle asserting that if P is a property of finite character then every
set has a β-maximal subset of which P holds. We show that these
principles and their variations have a wide range of strengths in the context
of second-order arithmetic, from being equivalent to Z2β to being
weaker than ACA0β and incomparable with WKL0β. In
particular, we identify a choice principle that, modulo Ξ£20β induction,
lies strictly below the atomic model theorem principle AMT and
implies the omitting partial types principle OPT