Axiom schema of specification
In many popular versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema. Essentially, it says that any definable subclass of a set is a set. Some mathematicians call it the axiom schema of comprehension, although others use that term for unrestricted comprehension, discussed below. Because restricting comprehension avoided Russell's paradox, several mathematicians including Zermelo, Fraenkel, and Gödel considered it the most important axiom of set theory.
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AussonderungsaxiomAxiom of abstractionAxiom of comprehensionAxiom of separationAxiom of specificationAxiom of subsetsAxiom schema of comprehensionAxiom schema of restricted comprehensionAxiom schema of separationAxiom schema of unrestricted comprehensionAxioms of subsetsComprehension axiomSubset axiomUnrestricted comprehensionUnrestricted comprehension principle
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Absolute InfiniteAckermann set theoryAffine logicAussonderungsaxiomAxiom of abstractionAxiom of comprehensionAxiom of empty setAxiom of infinityAxiom of limitation of sizeAxiom of pairingAxiom of regularityAxiom of separationAxiom of specificationAxiom of subsetsAxiom of unionAxiom schemaAxiom schema of comprehensionAxiom schema of predicative separationAxiom schema of replacementAxiom schema of restricted comprehensionAxiom schema of separationAxiom schema of unrestricted comprehensionAxioms of subsetsBertrand Russell's philosophical viewsBurali-Forti paradoxCantor's diagonal argumentCantor's theoremCartesian productComprehensionComprehension axiomConstructible universeConstructive set theoryControversy over Cantor's theoryCrispin WrightCurry's paradoxDiaconescu's theoremDialetheismEmpty setFrege's theoremGeneral set theory
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Axiom schema of specification
In many popular versions of axiomatic set theory, the axiom schema of specification, also known as the axiom schema of separation, subset axiom scheme or axiom schema of restricted comprehension is an axiom schema. Essentially, it says that any definable subclass of a set is a set. Some mathematicians call it the axiom schema of comprehension, although others use that term for unrestricted comprehension, discussed below. Because restricting comprehension avoided Russell's paradox, several mathematicians including Zermelo, Fraenkel, and Gödel considered it the most important axiom of set theory.
has abstract
Aksjomat podzbiorów, aksjomat ...... ule odpowiada osobny aksjomat.
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Das Aussonderungsaxiom stammt ...... ussonderungsschema bezeichnet.
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Delmängdsaxiomet är det axiom ...... erbar av en mängd är en mängd.
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In de axiomatische verzameling ...... die aan de eigenschap voldoen.
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In many popular versions of ax ...... important axiom of set theory.
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Le schéma d'axiomes de compréh ...... exprimer comme un seul axiome.
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Nella teoria degli insiemi, lo ...... tretta) menzionato più avanti.
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O Axioma da separação (também ...... iste um "axioma da separação".
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У теорії множин та області лог ...... ний підклас множини є множина.
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在公理化集合论和使用它的逻辑、数學和计算机科学分支中，分类公 ...... 有关的系统中，这个公理模式有时也限制于带有的公式，比如在中。
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Aksjomat podzbiorów, aksjomat ...... pewnym zbiorem (zawartym w A).
@pl
Das Aussonderungsaxiom stammt ...... ussonderungsschema bezeichnet.
@de
Delmängdsaxiomet är det axiom ...... erbar av en mängd är en mängd.
@sv
In de axiomatische verzameling ...... die aan de eigenschap voldoen.
@nl
In many popular versions of ax ...... important axiom of set theory.
@en
Le schéma d'axiomes de compréh ...... exprimer comme un seul axiome.
@fr
Nella teoria degli insiemi, lo ...... uesto è uno schema di assiomi.
@it
O Axioma da separação (também ...... iste um "axioma da separação".
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У теорії множин та області лог ...... ний підклас множини є множина.
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在公理化集合论和使用它的逻辑、数學和计算机科学分支中，分类公 ...... 质是： 一个通过一个谓词定义的集合的任何子类自身是一个集合。
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Aksjomat podzbiorów
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Aussonderungsaxiom
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Axiom schema of specification
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Axioma da separação
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Axiomaschema van afscheiding
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Delmängdsaxiomet
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Schema di assiomi di specificazione
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Schéma d'axiomes de compréhension
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Аксіомна схема виділення
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分类公理
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