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Mathematical Object

Von Neumann Universe

Logic, Foundations and Set Theory

The von Neumann universe, or von Neumann hierarchy of sets, denoted V, is the class of hereditary well-founded sets studied in set theory; formalized by Zermelo-Fraenkel set theory, it is often used to interpret or motivate that theory's own axioms. It is named after John von Neumann, though it was first published by Ernst Zermelo in 1930. Each well-founded set is assigned a rank, defined inductively as the smallest ordinal greater than the ranks of all of its members, and the sets making up V are organized into a transfinite, cumulative hierarchy indexed by that rank.

Facts
Classification
Object Kind
Set 1
Origin Year
1930 1
Connections

In Branch

Source Wikipedia: Von Neumann universe

Is Kind Of Object

Sets, Concepts

Entity-backed identity for the object-kind enum value this mathematical object already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The object-kind fact itself stays on the object unchanged.

Sources
1. Wikipedia: Von Neumann universe
  • History
    The first publication of the von Neumann universe was by Ernst Zermelo in 1930.
  • Introduction
    the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary well-founded sets.
  • In Branch: Set Theory, Lead sentence
    In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is th
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