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Lexikon


Zermelo set theory


ematics> A ef="module.php?name=Lexikon&file=search&eid=1&query=set theory">set theory with the following set of ef="module.php?name=Lexikon&file=search&eid=1&query=axiom">axioms: extensionality: two sets are equal if and only if they have the same elements. Union: If U is a set, so is the union of all its elements. Pair-set: If a and b are sets, so is ef="module.php?name=Lexikon&file=search&eid=1&query=a, b">a, b. Foundation: every set contains a set disjoint from itself. Comprehension (or Restriction): If P is a ef="module.php?name=Lexikon&file=search&eid=1&query=formula">formula with one ef="module.php?name=Lexikon&file=search&eid=1&query=free variable">free variable and X a set then ef="x">x: x is in X and P. is a set. Infinity: There exists an ef="module.php?name=Lexikon&file=search&eid=1&query=infinite set">infinite set. Power-set: If X is a set, so is its ef="module.php?name=Lexikon&file=search&eid=1&query=power set">power set. Zermelo set theory avoids ef="module.php?name=Lexikon&file=search&eid=1&query=Russell' s paradox">Russell' s paradox by excluding sets of elements with arbitrary properties - the Comprehension axiom only allows a property to be used to select elements of an existing set. ef="module.php?name=Lexikon&file=search&eid=1&query=Zermelo Fränkel set theory">Zermelo Fränkel set theory adds the Replacement axiom. [Other axioms?] (1995-03-30)

e="border-width:thin; border-color:#333333; border-style:dashed; padding:5px;" align="left">In addition suitable contents:
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[ 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=3136">dd ] [ ef="module.php?name=Lexikon&op=content&tid=3436">ding ] [ 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=3865">ec ] [ ef="module.php?name=Lexikon&op=content&tid=3896">ed ] [ ef="module.php?name=Lexikon&op=content&tid=3929">ee ] [ ef="module.php?name=Lexikon&op=content&tid=3953">eh ] [ 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=4273">excl ] [ 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=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=4828">fr ] [ ef="module.php?name=Lexikon&op=content&tid=4859">free ] [ ef="module.php?name=Lexikon&op=content&tid=4867">free variable ] [ 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=6103">infinite ] [ ef="module.php?name=Lexikon&op=content&tid=6107">infinite set ] [ ef="module.php?name=Lexikon&op=content&tid=6194">int ] [ ef="module.php?name=Lexikon&op=content&tid=6413">io ] [ 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=6681">jo ] [ ef="module.php?name=Lexikon&op=content&tid=6700">join ] [ ef="module.php?name=Lexikon&op=content&tid=6789">ke ] [ 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=7415">lu ] [ ef="module.php?name=Lexikon&op=content&tid=7441">ly ] [ 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=8228">ms ] [ ef="module.php?name=Lexikon&op=content&tid=8258">mu ] [ ef="module.php?name=Lexikon&op=content&tid=8386">na ] [ ef="module.php?name=Lexikon&op=content&tid=8472">ne ] [ 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=8660">nl ] [ 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=9014">op ] [ ef="module.php?name=Lexikon&op=content&tid=9204">pa ] [ ef="module.php?name=Lexikon&op=content&tid=9270">paradox ] [ ef="module.php?name=Lexikon&op=content&tid=9457">pe ] [ 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=9908">pr ] [ 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=10907">Russell ] [ ef="module.php?name=Lexikon&op=content&tid=10922">sa ] [ ef="module.php?name=Lexikon&op=content&tid=10959">sam ] [ 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=11509">sj ] [ 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=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=12939">tw ] [ ef="module.php?name=Lexikon&op=content&tid=12986">ua ] [ ef="module.php?name=Lexikon&op=content&tid=13076">union ] [ ef="module.php?name=Lexikon&op=content&tid=13175">us ] [ ef="module.php?name=Lexikon&op=content&tid=13252">va ] [ ef="module.php?name=Lexikon&op=content&tid=13274">var ] [ ef="module.php?name=Lexikon&op=content&tid=13275">variable ] [ ef="module.php?name=Lexikon&op=content&tid=13310">ve ] [ ef="module.php?name=Lexikon&op=content&tid=13725">win ] [ ef="module.php?name=Lexikon&op=content&tid=13877">ws ] [ 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=14099">Zermelo Fränkel set theory ]






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