KnowraCumulative hierarchyLinked fromLinked fromThe 14 pages that link to Cumulative hierarchy, each with the reason it gives.All 14Broader topic 3Related 9Narrower topic 2Zermelo–Fraenkel set theoryNarrower topic: It offers a model of the universe of sets that reflects Foundation and Power Set.Well-founded relationBroader topic: Its rank construction relies on foundation and recursion along well-founded membership.Axiom of unionRelated: At limit stages, the hierarchy gathers all sets formed at earlier stages by union.Axiom of FoundationRelated: Foundation supports the view that every set appears at some stage of this hierarchy.Transfinite recursionBroader topic: Its stages are defined directly by transfinite recursion along the ordinals.Axiom of constructibilityNarrower topic: V = L identifies the full cumulative universe with a more selective hierarchy.Membership relationRelated: It organizes sets according to the membership relations among their elements.Axiom of Power SetRelated: The axiom supplies the successor-stage operation in this standard model of set theory.Large cardinalRelated: Large-cardinal properties often describe how the universe of sets behaves around particular levels.Von Neumann universeRelated: This is the construction that organizes the universe into levels.Axiom of regularityRelated: Regularity ensures every set belongs to some stage of this hierarchy.Axiom schema of replacementRelated: Replacement helps ensure that stages indexed by a set of ordinals can be gathered into a set.Axiom of global choiceRelated: A global selector can choose elements uniformly across sets appearing at every hierarchy level.Universe (mathematics and logic)Broader topic: It organizes the standard set-theoretic universe into levels of increasing complexity.