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Lexikon


von Neumann ordinal


ematics> An implementation of ef="module.php?name=Lexikon&file=search&eid=1&query=ordinals">ordinals in ef="module.php?name=Lexikon&file=search&eid=1&query=set theory">set theory (e.g. ef="module.php?name=Lexikon&file=search&eid=1&query=Zermelo Fränkel set theory">Zermelo Fränkel set theory or ef="module.php?name=Lexikon&file=search&eid=1&query=ZFC">ZFC). The von Neumann ordinal alpha is the ef="module.php?name=Lexikon&file=search&eid=1&query=well-ordered set">well-ordered set containing just the ordinals "shorter" than alpha. "Reasonable" set theories (like ZF) include Mostowski' s Collapsing Theorem: any ef="module.php?name=Lexikon&file=search&eid=1&query=well-ordered set">well-ordered set is ef="module.php?name=Lexikon&file=search&eid=1&query=isomorphic">isomorphic to a von Neumann ordinal. In really screwy theories (e.g. NFU -- New Foundations with Urelemente) this theorem is false. The finite von Neumann ordinals are the {von Neumann integers}. (1995-03-30)

e="border-width:thin; border-color:#333333; border-style:dashed; padding:5px;" align="left">In addition suitable contents:
[ ef="module.php?name=Lexikon&op=content&tid=134">= ] [ ef="module.php?name=Lexikon&op=content&tid=411">ai ] [ ef="module.php?name=Lexikon&op=content&tid=433">al ] [ ef="module.php?name=Lexikon&op=content&tid=544">am ] [ ef="module.php?name=Lexikon&op=content&tid=592">an ] [ ef="module.php?name=Lexikon&op=content&tid=740">ar ] [ ef="module.php?name=Lexikon&op=content&tid=743">arc ] [ ef="module.php?name=Lexikon&op=content&tid=800">as ] [ ef="module.php?name=Lexikon&op=content&tid=894">at ] [ ef="module.php?name=Lexikon&op=content&tid=1026">b ] [ ef="module.php?name=Lexikon&op=content&tid=1708">C ] [ ef="module.php?name=Lexikon&op=content&tid=2001">ch ] [ ef="module.php?name=Lexikon&op=content&tid=2138">cl ] [ ef="module.php?name=Lexikon&op=content&tid=2247">co ] [ ef="module.php?name=Lexikon&op=content&tid=2545">con ] [ ef="module.php?name=Lexikon&op=content&tid=2791">cr ] [ ef="module.php?name=Lexikon&op=content&tid=3151">de ] [ ef="module.php?name=Lexikon&op=content&tid=3752">du ] [ ef="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ef="module.php?name=Lexikon&op=content&tid=3946">eg ] [ ef="module.php?name=Lexikon&op=content&tid=4008">element ] [ ef="module.php?name=Lexikon&op=content&tid=4148">er ] [ ef="module.php?name=Lexikon&op=content&tid=4171">es ] [ ef="module.php?name=Lexikon&op=content&tid=4199">et ] [ ef="module.php?name=Lexikon&op=content&tid=4432">FC ] [ ef="module.php?name=Lexikon&op=content&tid=4497">fi ] [ ef="module.php?name=Lexikon&op=content&tid=4520">file ] [ ef="module.php?name=Lexikon&op=content&tid=4559">finite ] [ ef="module.php?name=Lexikon&op=content&tid=5057">ge ] [ ef="module.php?name=Lexikon&op=content&tid=5434">h ] [ ef="module.php?name=Lexikon&op=content&tid=5768">hr ] [ ef="module.php?name=Lexikon&op=content&tid=5931">id ] [ ef="module.php?name=Lexikon&op=content&tid=5956">ie ] [ ef="module.php?name=Lexikon&op=content&tid=6013">il ] [ ef="module.php?name=Lexikon&op=content&tid=6064">in ] [ ef="module.php?name=Lexikon&op=content&tid=6068">inc ] [ ef="module.php?name=Lexikon&op=content&tid=6070">include ] [ ef="module.php?name=Lexikon&op=content&tid=6194">int ] [ ef="module.php?name=Lexikon&op=content&tid=6196">integer ] [ ef="module.php?name=Lexikon&op=content&tid=6413">io ] [ ef="module.php?name=Lexikon&op=content&tid=6482">is ] [ ef="module.php?name=Lexikon&op=content&tid=6542">isomorphic ] [ ef="module.php?name=Lexikon&op=content&tid=6558">it ] [ ef="module.php?name=Lexikon&op=content&tid=6789">ke ] [ ef="module.php?name=Lexikon&op=content&tid=6822">ki ] [ ef="module.php?name=Lexikon&op=content&tid=6918">la ] [ ef="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ ef="module.php?name=Lexikon&op=content&tid=7107">li ] [ ef="module.php?name=Lexikon&op=content&tid=7399">ls ] [ ef="module.php?name=Lexikon&op=content&tid=7415">lu ] [ ef="module.php?name=Lexikon&op=content&tid=7441">ly ] [ ef="module.php?name=Lexikon&op=content&tid=7457">M ] [ ef="module.php?name=Lexikon&op=content&tid=7463">ma ] [ ef="module.php?name=Lexikon&op=content&tid=7582">man ] [ ef="module.php?name=Lexikon&op=content&tid=8032">mo ] [ ef="module.php?name=Lexikon&op=content&tid=8040">mod ] [ ef="module.php?name=Lexikon&op=content&tid=8079">module ] [ ef="module.php?name=Lexikon&op=content&tid=8167">mp ] [ ef="module.php?name=Lexikon&op=content&tid=8384">N ] [ ef="module.php?name=Lexikon&op=content&tid=8386">na ] [ ef="module.php?name=Lexikon&op=content&tid=8460">nc ] [ ef="module.php?name=Lexikon&op=content&tid=8627">ng ] [ ef="module.php?name=Lexikon&op=content&tid=8630">ni ] [ ef="module.php?name=Lexikon&op=content&tid=8672">nn ] [ ef="module.php?name=Lexikon&op=content&tid=8760">ns ] [ ef="module.php?name=Lexikon&op=content&tid=8964">om ] [ ef="module.php?name=Lexikon&op=content&tid=9116">ordinal ] [ ef="module.php?name=Lexikon&op=content&tid=9550">ph ] [ ef="module.php?name=Lexikon&op=content&tid=9651">pl ] [ ef="module.php?name=Lexikon&op=content&tid=10253">query ] [ ef="module.php?name=Lexikon&op=content&tid=10364">rc ] [ ef="module.php?name=Lexikon&op=content&tid=10385">re ] [ ef="module.php?name=Lexikon&op=content&tid=10390">real ] [ ef="module.php?name=Lexikon&op=content&tid=11010">sc ] [ ef="module.php?name=Lexikon&op=content&tid=11097">screw ] [ ef="module.php?name=Lexikon&op=content&tid=11150">se ] [ ef="module.php?name=Lexikon&op=content&tid=11281">set ] [ ef="module.php?name=Lexikon&op=content&tid=11292">set theory ] [ ef="module.php?name=Lexikon&op=content&tid=11314">sh ] [ ef="module.php?name=Lexikon&op=content&tid=11376">si ] [ ef="module.php?name=Lexikon&op=content&tid=11510">sk ] [ ef="module.php?name=Lexikon&op=content&tid=11651">so ] [ ef="module.php?name=Lexikon&op=content&tid=11934">st ] [ ef="module.php?name=Lexikon&op=content&tid=12359">T ] [ ef="module.php?name=Lexikon&op=content&tid=12588">th ] [ ef="module.php?name=Lexikon&op=content&tid=12602">theory ] [ ef="module.php?name=Lexikon&op=content&tid=12721">to ] [ ef="module.php?name=Lexikon&op=content&tid=13030">um ] [ ef="module.php?name=Lexikon&op=content&tid=13175">us ] [ ef="module.php?name=Lexikon&op=content&tid=13503">von Neumann integer ] [ ef="module.php?name=Lexikon&op=content&tid=13667">well-ordered set ] [ ef="module.php?name=Lexikon&op=content&tid=13877">ws ] [ ef="module.php?name=Lexikon&op=content&tid=14079">Z ] [ ef="module.php?name=Lexikon&op=content&tid=14099">Zermelo Fränkel set theory ] [ ef="module.php?name=Lexikon&op=content&tid=14113">ZFC ]






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