# 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
