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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.
5
votes
Ultrainfinitism, or a step beyond the transfinite
You might like the peculiar set theory NFU (Quine New Foundation, but with atoms)
extended with axioms which are quite natural in the NFU context and that turn out
to be equiconsistent with ZFC plus s …