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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.
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Explaining the consistency of PRA and ZF from predicative foundations
Recently I got interested in predicative foundations, mostly because of Laura Crosilla's work and because Agda employs a predicative type theory. … Impredicative foundations such as PRA or ZF seem to be consistent. …
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Explaining the consistency of PRA and ZF from predicative foundations
Last week, I learned from Ulrik Buchholtz that there are proof-theoretic reductions from certain impredicative systems to certain predicative ones. While these fall short of predicatively explaining t …