Highly Influential

Weprove in set theory without the Axiom of Choice, that Rado’s selection lemma (RL) implies the Hahn-Banach axiom. We also prove that RL is equivalent to several consequences of the Tychonov theorem for compact Hausdorff spaces: in particular,RL implies that every filter on awell orderable set is included in a ultrafilter. In set theory with atoms, the… (More)