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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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Is there a metamathematical $V$?

(taken from a comment) To me, the idea of ordinals being a completed infinity contradicts the idea of ordinals (I mean the informal idea of ordinals, that is, that after every "completed collection" o …
Akiva Weinberger's user avatar