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From English Wikipedia @ Freddythechick
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Major topics in
Foundations 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
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