+++
title = "Different logical foundations"
author = "Yann Herklotz"
tags = []
categories = []
backlinks = ["4c"]
forwardlinks = ["4c2"]
zettelid = "4c1"
+++

There are different logical foundations to mathematics. The main one
that is used is Zermelo-Fraenkel set theory with the axiom of choice
(ZFC). However, there can be alternatives. For example, type theory
provides and alternative basis for the theory of mathematics, and also
result in a different logic.

Propositional logic always needs set theory as a base to work with,
however, logical systems like intuitionistic logic can be built up using
type theory without ever needing set theory.