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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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How much larger is the powerset of a transfinite set?
This may seem a vague question, but in the process of explaining the hierarchy of transfinite sets to my students, I've had to use the Cardinality(powerset(S)) > Cardinality(S) argument, which appeare …