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v • d • e Major topics in Foundations of Mathematics Mathematical logic Peano axioms • Mathematical induction • Axiomatic system • Mathematical proof • Model theory • Mathematical constructivism • Modal logic • List of mathematical logic topics Set theory Set • Naive set theory • Axiomatic set theory • Zermelo set theory • Zermelo-Fraenkel set theory • Descriptive set theory • Determinacy • Russell's paradox • List of set theory topics Category theory Category • Type theory • Topos theory • Glossary of category theory • List of category theory topics