Editing Axiom of constructibility (section)

{{short description|Possible axiom for set theory in mathematics}}
{{no footnotes|date=May 2017}}
The '''axiom of constructibility''' is a possible [[axiom]] for [[set theory]] in mathematics that asserts that every set is [[constructible universe|constructible]]. The axiom is usually written as '''''V'' = ''L'''''. The axiom, first investigated by [[Kurt Gödel]], is inconsistent with the proposition that [[zero sharp]] exists and stronger [[large cardinal axiom]]s (see [[list of large cardinal properties]]). Generalizations of this axiom are explored in [[inner model theory]].<ref>{{Cite web |last=Hamkins |first=Joel David |date=February 27, 2015 |title=Embeddings of the universe into the constructible universe, current state of knowledge, CUNY Set Theory Seminar, March 2015 |url=https://jdh.hamkins.org/tag/constructible-universe/ |url-status=live |archive-url=https://web.archive.org/web/20240423205201/https://jdh.hamkins.org/tag/constructible-universe/ |archive-date=April 23, 2024 |access-date=September 22, 2024 |website=[[Joel David Hamkins|jdh.hamkins.org]] |language=en-US}}</ref>