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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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What do models where the CH is false look like?
You must start slightly further back. The Axiom of Choice (AC) and the Axiom of Determinacy (AD) are both very desirable, but contradict one another. We usually feel AC has more claim to truth since …