DOI: 10.4324/9780415249126-Y029-1
Version: v1, Published online: 1998
Retrieved April 27, 2024, from https://www.rep.routledge.com/articles/thematic/the-constructible-universe/v-1
Version: v1, Published online: 1998
Retrieved April 27, 2024, from https://www.rep.routledge.com/articles/thematic/the-constructible-universe/v-1
Article Summary
the ‘universe’ of constructible sets was introduced by Kurt Gödel in order to prove the consistency of the axiom of choice (AC) and the continuum hypothesis (CH) with the basic (ZF) axioms of set theory. The hypothesis that all sets are constructible is the axiom of constructibility (V = L). Gödel showed that if ZF is consistent, then ZF + V = L is consistent, and that AC and CH are provable in ZF + V = L.
Citing this article:
Burgess, John P.. The constructible universe, 1998, doi:10.4324/9780415249126-Y029-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/the-constructible-universe/v-1.
Copyright © 1998-2024 Routledge.
Burgess, John P.. The constructible universe, 1998, doi:10.4324/9780415249126-Y029-1. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/the-constructible-universe/v-1.
Copyright © 1998-2024 Routledge.