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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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Set-theoretic foundations for formal language theory?
For the foundations of formal language theory, the following ideas show up:
Universal algebra (here for 'free' monoids and basic logic involving simple equation only proofs, just variables and no c …