> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/100-fundamentals/120-foundations-of-mathematics/list-of-fom-candidates.md).

# The list of FOM candidates

The foundation of mathematics is a field of math that deals with establishing a theory to serve as the foundations of the entire math, from which theentirety ofmath may be derived.

Some theories were developed especially for this purpose, and others, already existing theories are probed as the candidates.

Math foundations candidates:

* Set theory
  * ZF set theory
  * BG set theory
* Primitive Recursive Functions
* Combinatory logic
* Type theory
  * Typed λ-calculus by Alonzo Church
  * Intuitionistic type theory by Per Martin-Löf
  * univalent type theory
* Category theory