Zermelo Fränkel set theory
ematics> A ef="module.php?name=Lexikon&file=search&eid=1&query=set theory">set theory with the ef="module.php?name=Lexikon&file=search&eid=1&query=axiom">axioms of {Zermelo set theory} (extensionality, Union, Pair-set, Foundation, Restriction, Infinity, Power-set) plus the Replacement {axiom schema}: If F(x,y) is a ef="module.php?name=Lexikon&file=search&eid=1&query=formula">formula such that for any x, there is a unique y making F true, and X is a set, then ef="module.php?name=Lexikon&file=search&eid=1&query=F x : x in X">F x : x in X is a set. In other words, if you do something to each element of a set, the result is a set. An important but controversial ef="module.php?name=Lexikon&file=search&eid=1&query=axiom">axiom which is NOT part of ZF theory is the ef="module.php?name=Lexikon&file=search&eid=1&query=Axiom of Choice">Axiom of Choice. (1995-04-10) 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=894">at ] [ ef="module.php?name=Lexikon&op=content&tid=1013">axiom ] [ ef="module.php?name=Lexikon&op=content&tid=1018">Axiom of Choice ] [ 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=2000">Ch ] [ ef="module.php?name=Lexikon&op=content&tid=2001">ch ] [ 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=3565">do ] [ ef="module.php?name=Lexikon&op=content&tid=3752">du ] [ ef="module.php?name=Lexikon&op=content&tid=3834">e ] [ 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=4497">fi ] [ ef="module.php?name=Lexikon&op=content&tid=4520">file ] [ ef="module.php?name=Lexikon&op=content&tid=4700">fo ] [ ef="module.php?name=Lexikon&op=content&tid=4727">for ] [ ef="module.php?name=Lexikon&op=content&tid=4757">formula ] [ ef="module.php?name=Lexikon&op=content&tid=5434">h ] [ ef="module.php?name=Lexikon&op=content&tid=5540">hat ] [ ef="module.php?name=Lexikon&op=content&tid=5656">hing ] [ 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=6013">il ] [ ef="module.php?name=Lexikon&op=content&tid=6053">import ] [ ef="module.php?name=Lexikon&op=content&tid=6064">in ] [ ef="module.php?name=Lexikon&op=content&tid=6413">io ] [ ef="module.php?name=Lexikon&op=content&tid=6446">iq ] [ ef="module.php?name=Lexikon&op=content&tid=6449">ir ] [ ef="module.php?name=Lexikon&op=content&tid=6482">is ] [ ef="module.php?name=Lexikon&op=content&tid=6558">it ] [ 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=7410">lt ] [ ef="module.php?name=Lexikon&op=content&tid=7415">lu ] [ ef="module.php?name=Lexikon&op=content&tid=7463">ma ] [ 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=8258">mu ] [ 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=8622">nf ] [ 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=8728">NOT ] [ ef="module.php?name=Lexikon&op=content&tid=8760">ns ] [ ef="module.php?name=Lexikon&op=content&tid=8820">O ] [ ef="module.php?name=Lexikon&op=content&tid=8964">om ] [ ef="module.php?name=Lexikon&op=content&tid=9160">OT ] [ ef="module.php?name=Lexikon&op=content&tid=9204">pa ] [ 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=9736">plus ] [ ef="module.php?name=Lexikon&op=content&tid=9821">port ] [ 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=10767">ro ] [ ef="module.php?name=Lexikon&op=content&tid=10887">ru ] [ ef="module.php?name=Lexikon&op=content&tid=11010">sc ] [ 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=11376">si ] [ 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=12090">strict ] [ ef="module.php?name=Lexikon&op=content&tid=12133">su ] [ 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=12787">tr ] [ ef="module.php?name=Lexikon&op=content&tid=13175">us ] [ ef="module.php?name=Lexikon&op=content&tid=13310">ve ] [ ef="module.php?name=Lexikon&op=content&tid=13820">word ] [ ef="module.php?name=Lexikon&op=content&tid=13891">X ] [ ef="module.php?name=Lexikon&op=content&tid=14079">Z ] [ ef="module.php?name=Lexikon&op=content&tid=14100">Zermelo set theory ]
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