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first-order and higher-order logic, model theory, set theory, proof theory, computability theory, formal languages, definability, interplay of syntax and semantics, constructive logic, intuitionism, philosophical logic, modal logic, completeness, Gödel incompleteness, decidability, undecidability, theories of truth, truth revision, consistency.
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 …