KnowraGödel's constructible universeLinked fromLinked fromThe 17 pages that link to Gödel's constructible universe, each with the reason it gives.All 17Broader topic 2Related 9Narrower topic 1Compared with 5Set theoryRelated: It was used to show that the continuum hypothesis and axiom of choice are consistent with Zermelo–Fraenkel set theory, if that theory is consistent.Georg CantorRelated: Gödel used it to show that the continuum hypothesis cannot be disproved from ZFC, if ZFC is consistent.Continuum hypothesisRelated: Gödel used it to show the continuum hypothesis cannot be disproved from ZFC, if ZFC is consistent.Cumulative hierarchyRelated: It adapts the hierarchy by admitting only sets definable at each stage.CompletenessRelated: Gödel's work on completeness also included a completeness result for quantified modal logic using this framework.Axiom of infinityRelated: It provides a model of set theory with infinity, demonstrating consistency relative to suitable assumptions.Aleph numberRelated: Gödel showed that the generalized continuum hypothesis is consistent with set theory if set theory is consistent.Axiom schema of replacementRelated: Replacement is among the axioms whose validity Gödel established in the constructible universe.Axiom of global choiceRelated: Its canonical well-order provides a definable source of global choices within the model.