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- Oct 2024
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Cohen (Independence of the Axiomof Choice; The Independence of the Continuum Hypothesis I, I1) completed theproof of independence for each by showing neither could be deduced from theexisting axioms (by showing the negation of each could consistently be added tothe Zermelo—Fraenkel axiom scheme). See P. J. Cohen (Set Theory and theContinuum Hypothesis) for a discussion of these results and his intuition about thecontinuum hypothesis. Another expository reference is Cohen (IndependenceResults in Set Theory).
In 1963 Paul Cohen completed the work of Gödel by proving the independence of the axiom of choice and the continuum hypothesis from the Zermelo-Fraenkel set theory axioms. He did this by showing that neither could be deduced from the existing axioms and specifically by showing that the negation of each could be added to ZF consistently.
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