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Mathematical logic, Set theory, Peano arithmetic, Model theory, Proof theory, Recursion theory, Computability theory, Univalent foundations, Reverse mathematics, Frege foundation of arithmetic, Goedel's incompleteness and Mathematics, Structural set theory, Category theory, Type 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 …