Linked from

The 17 pages that link to Gödel's constructible universe, each with the reason it gives.

• Set 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.

• Forcing (mathematics)Compared with: It proves relative consistency by restricting attention to an inner model rather than adding sets.

• Transfinite recursionBroader topic: The levels Lα are formed by a recursive successor rule and unions at limits.

• Axiom of constructibilityBroader topic: V = L says that this internally generated class contains every set.

• Axiom of infinityRelated: It provides a model of set theory with infinity, demonstrating consistency relative to suitable assumptions.

• Gödel sentenceCompared with: Despite sharing Gödel’s name, this is a separate construction in set theory, not an incompleteness sentence.

• Large cardinalCompared with: L satisfies choice and has no large cardinals, illustrating how restrictive a canonical inner model can be.

• Von Neumann universeCompared with: Unlike the full hierarchy, it retains only constructible sets.

• 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.

• Solovay modelCompared with: It provides a contrasting setting in which the axiom of choice holds.

• Axiom of global choiceRelated: Its canonical well-order provides a definable source of global choices within the model.

• Diamond principleNarrower topic: Diamond holds in L, revealing the principle’s connection to highly organized set-theoretic universes.