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- Von_Neumann_universe abstract "In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted V, is the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation of the axioms of ZFC.The rank of a well-founded set is defined inductively as the smallest ordinal number greater than the ranks of all members of the set. In particular, the rank of the empty set is zero, and every ordinal has a rank equal to itself. The sets in V are divided into a transfinite hierarchy, called the cumulative hierarchy, based on their rank.".
- Von_Neumann_universe thumbnail Von_Neumann_universe_4.png?width=300.
- Von_Neumann_universe wikiPageExternalLink newmann.html.
- Von_Neumann_universe wikiPageExternalLink view?rid=ensmat-001:1917:19::9&id=hitlist.
- Von_Neumann_universe wikiPageExternalLink ?PPN=PPN266833020_0027&DMDID=DMDLOG_0042.
- Von_Neumann_universe wikiPageExternalLink arithmeticespri00peangoog.
- Von_Neumann_universe wikiPageID "445980".
- Von_Neumann_universe wikiPageLength "16024".
- Von_Neumann_universe wikiPageOutDegree "51".
- Von_Neumann_universe wikiPageRevisionID "707830457".
- Von_Neumann_universe wikiPageWikiLink Aczels_anti-foundation_axiom.
- Von_Neumann_universe wikiPageWikiLink Axiom_of_infinity.
- Von_Neumann_universe wikiPageWikiLink Axiom_of_regularity.
- Von_Neumann_universe wikiPageWikiLink Axiom_schema_of_replacement.
- Von_Neumann_universe wikiPageWikiLink Category:Set-theoretic_universes.
- Von_Neumann_universe wikiPageWikiLink Class_(set_theory).
- Von_Neumann_universe wikiPageWikiLink Constructible_universe.
- Von_Neumann_universe wikiPageWikiLink Cumulative_hierarchy.
- Von_Neumann_universe wikiPageWikiLink Empty_set.
- Von_Neumann_universe wikiPageWikiLink Ernst_Zermelo.
- Von_Neumann_universe wikiPageWikiLink Grothendieck_universe.
- Von_Neumann_universe wikiPageWikiLink Gxc3xb6dels_incompleteness_theorems.
- Von_Neumann_universe wikiPageWikiLink Hereditarily_finite_set.
- Von_Neumann_universe wikiPageWikiLink Hereditary_set.
- Von_Neumann_universe wikiPageWikiLink Inaccessible_cardinal.
- Von_Neumann_universe wikiPageWikiLink John_von_Neumann.
- Von_Neumann_universe wikiPageWikiLink Limit_ordinal.
- Von_Neumann_universe wikiPageWikiLink Mathematics.
- Von_Neumann_universe wikiPageWikiLink Mathematische_Zeitschrift.
- Von_Neumann_universe wikiPageWikiLink Model_theory.
- Von_Neumann_universe wikiPageWikiLink Morse–Kelley_set_theory.
- Von_Neumann_universe wikiPageWikiLink Natural_number.
- Von_Neumann_universe wikiPageWikiLink Observable_universe.
- Von_Neumann_universe wikiPageWikiLink Ordinal_number.
- Von_Neumann_universe wikiPageWikiLink Power_set.
- Von_Neumann_universe wikiPageWikiLink S_(set_theory).
- Von_Neumann_universe wikiPageWikiLink Set_theory.
- Von_Neumann_universe wikiPageWikiLink Structure_(mathematical_logic).
- Von_Neumann_universe wikiPageWikiLink Transfinite_induction.
- Von_Neumann_universe wikiPageWikiLink Union_(set_theory).
- Von_Neumann_universe wikiPageWikiLink Universal_set.
- Von_Neumann_universe wikiPageWikiLink Universe_(mathematics).
- Von_Neumann_universe wikiPageWikiLink Urelement.
- Von_Neumann_universe wikiPageWikiLink Virginia_Commonwealth_University.
- Von_Neumann_universe wikiPageWikiLink Well-founded_relation.
- Von_Neumann_universe wikiPageWikiLink Zermelo_set_theory.
- Von_Neumann_universe wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Von_Neumann_universe wikiPageWikiLink File:Von_Neumann_universe_4.png.
- Von_Neumann_universe wikiPageWikiLinkText "''V''".
- Von_Neumann_universe wikiPageWikiLinkText "V".
- Von_Neumann_universe wikiPageWikiLinkText "Von Neumann universe".
- Von_Neumann_universe wikiPageWikiLinkText "class of all sets".
- Von_Neumann_universe wikiPageWikiLinkText "cumulative hierarchy".
- Von_Neumann_universe wikiPageWikiLinkText "iterative hierarchy".
- Von_Neumann_universe wikiPageWikiLinkText "rank".
- Von_Neumann_universe wikiPageWikiLinkText "universe of sets".
- Von_Neumann_universe wikiPageWikiLinkText "universe".
- Von_Neumann_universe wikiPageWikiLinkText "von Neumann hierarchy of sets".
- Von_Neumann_universe wikiPageWikiLinkText "von Neumann hierarchy".
- Von_Neumann_universe wikiPageWikiLinkText "von Neumann universe".
- Von_Neumann_universe wikiPageUsesTemplate Template:Citation.
- Von_Neumann_universe wikiPageUsesTemplate Template:Cite_book.
- Von_Neumann_universe wikiPageUsesTemplate Template:Cite_journal.
- Von_Neumann_universe wikiPageUsesTemplate Template:Reflist.
- Von_Neumann_universe subject Category:Set-theoretic_universes.
- Von_Neumann_universe hypernym Sets.
- Von_Neumann_universe type Train.
- Von_Neumann_universe type Redirect.
- Von_Neumann_universe comment "In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted V, is the class of hereditary well-founded sets. This collection, which is formalized by Zermelo–Fraenkel set theory (ZFC), is often used to provide an interpretation or motivation of the axioms of ZFC.The rank of a well-founded set is defined inductively as the smallest ordinal number greater than the ranks of all members of the set.".
- Von_Neumann_universe label "Von Neumann universe".
- Von_Neumann_universe sameAs Q77887.
- Von_Neumann_universe sameAs Von-Neumann-Hierarchie.
- Von_Neumann_universe sameAs フォン・ノイマン宇宙.
- Von_Neumann_universe sameAs 폰_노이만_전체.
- Von_Neumann_universe sameAs Universo_de_von_Neumann.
- Von_Neumann_universe sameAs m.029dwt.
- Von_Neumann_universe sameAs Универсум_фон_Неймана.
- Von_Neumann_universe sameAs Q77887.
- Von_Neumann_universe sameAs 冯·诺伊曼全集.
- Von_Neumann_universe wasDerivedFrom Von_Neumann_universe?oldid=707830457.
- Von_Neumann_universe depiction Von_Neumann_universe_4.png.
- Von_Neumann_universe isPrimaryTopicOf Von_Neumann_universe.