---
tag: ZCXNR881FX
kind: concept
name: Constructive set theory
aliases: [czf, constructivist-set-theory, izf, intuitionistic-zermelo-fraenkel, intuitionistic-set-theory, myhills-constructive-set-theory]
sources:
  - wikipedia: en:5042360@r1365499298
    locator: Constructive set theory
    note: adopted
    mention: wikipedia://en/5042360
    sections: [Summary]
same_as:
  wikidata: Q5164501
  wikipedia: Constructive set theory
inventory: [W4P68BG1TY]
---

## Summary

Axiomatic **constructive set theory** is an approach to mathematical constructivism following the program of axiomatic set theory. The same [[first-order|086QKPF0A6]] language with "$=$" and "$\in$" of classical set theory is usually used, so this is not to be confused with a constructive types approach. On the other hand, some constructive theories are indeed motivated by their interpretability in type theories.