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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 do we avoid circularity when we build a structure for ZFC?
From the point of view of mathematics, we are not in the circle. We are using the language of set theory for expressing our definitions, theorems and proofs, because we know how good and suitable this …