KnowraCumulative hierarchyLinked fromLinked fromThe 14 pages that link to Cumulative hierarchy, each with the reason it gives.All 14Broader topic 3Related 9Narrower topic 2Axiom 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.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.