The Axiom of Constructibility: A Guide for the Mathematician (Lecture Notes in Mathematics) by Keith Devlin (3540085203)

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Now, there is nothing wrong about assuming the Axiom of Choice. But let us be sure about one thing: we are making an assumption here. We are saying, in effect, that when we speak of ''set theory", the Axiom of Choice is one of the basic properties of sets which we intend to use. This is a perfectly reasonable assumption to make, as most pure mathematicians would agree. Horeover (and here we are at a distinct advantage over those who first advocated the use of the Axiom of Choice), we know for sure that assuming the Axiom of Choice does not lead to a contradiction with our other (more fundamental) assumptions about sets.

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