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v t e Major topics inFoundations of Mathematics
Mathematical logic	Peano axioms Mathematical induction Formal system Axiomatic system Hilbert system Natural deduction 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 Constructive set theory Descriptive set theory Determinacy Russell's paradox List of set theory topics
Type theory	Axiom of reducibility Simple type theory Dependent type theory Intuitionistic type theory Homotopy type theory Univalent foundations Girard's paradox
Category theory	Category Topos theory Category of sets Higher category theory ∞-groupoid ∞-topos theory Mathematical structuralism Glossary of category theory List of category theory topics