The foundation of mathematics

• The foundations of mathematics

• foundational crisis of mathematics

• logicism

• candidate theories for TFOM

• implementation of mathematics in set theory

• Hilbert's problems, Hilbert's program

• Axiomatization of mathematics

Major topics in Foundations of Mathematics (FOM)

Major topics in FOM

• Mathematical logic

  • Peano axioms

  • Mathematical induction

  • Formal system

    • Axiomatic system

    • Hilbert system

    • Natural deduction

  • Mathematical proof

  • Model theory

  • Mathematical constructivism

  • Modal logic

• 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

• Type theory

  • Axiom of reducibility

  • Girard's paradox

  • Simple type theory

  • Dependent type theory

  • Intuitionistic type theory

  • Homotopy type theory

  • Univalent foundations

• Category theory

  • Category

  • Topos theory

  • Category of sets

  • Higher category theory

  • ∞-groupoid

  • ∞-topos theory

  • Mathematical structuralism

https://en.wikipedia.org/wiki/List_of_mathematical_logic_topics https://en.wikipedia.org/wiki/List_of_set_theory_topics https://en.wikipedia.org/wiki/List_of_category_theory_topics https://en.wikipedia.org/wiki/Glossary_of_category_theory