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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.
2
votes
What practical applications does set theory have?
As a working mathematician, not as a logician what I am not, set theory is the set (!) of rules in order to use the symbol $\in$, meaning "belongs to". That tells me when and how I can use it.
EDIT: …