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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.

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5 answers
2k views

Decidability of the Axiom of Choice

Everything that I read regarding Set Theory states that the Axiom of Choice is independent and undecidable within the context of Zermelo-Frankel Set Theory. My question is this: Is there any consisten …