From: Norman D. Megill Subject: Re: A question on Set Theory Date: 16 Apr 2000 04:21:13 -0400 Newsgroups: sci.math.research Summary: [missing] In article <38F85A23.B5B13295@algebra.uni-linz.ac.at>, Franz Binder wrote: [...] >But there are more possibilietes that make sense (thus no canonical >one), e.g., >1) A=B iff there is a bijection between them >2) A=B iff there is an injection in both directions >Note that Bernstein's lemma is not true in the constructive context >(need Axiom of Choice). Although "Bernstein's lemma" (Schroeder-Bernstein theorem?) has a much shorter proof using AC, it does not need it and can be proved using only the following axioms of ZF set theory: Extensionality, Replacement, Union, and Power. Not even Infinity is needed. --Norm