Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets free of paradoxes such as Russell's paradox. Zermelo–Fraenkel set theory with the historically controversial axiom of choice included is commonly abbreviated ZFC, where C stands for choice. Many authors use ZF to refer to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded. Today ZFC is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.
known for
Axioms of ZFZFCZFC Set TheoryZFC Set theoryZFC setZFC set theoryZF axiomsZF set theoryZermelo-FraenkelZermelo-Fraenkel-Skolem set theoryZermelo-Fraenkel axiomZermelo-Fraenkel axiomatizationZermelo-Fraenkel axiomsZermelo-Fraenkel frameworkZermelo-Fraenkel set theoryZermelo-Fraenkel set theory with the axiom of choiceZermelo-FrankelZermelo-Frankel axiomZermelo-Frankel axiomsZermelo-Frankel set theoryZermelo-FränkelZermelo-Fränkel set theoryZermelo-frankelZermelo Fraenkel set theoryZermelo–FraenkelZermelo–Fraenkel axiomZermelo–Fraenkel axiomatizationZermelo–Fraenkel axiomsZermelo–Fraenkel frameworkZermelo–Fraenkel set theory with the axiom of choiceZermelo–Frankel set theoryZermelo−Fraenkel set theoryZfc
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Zermelo–Fraenkel set theory
In mathematics, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is one of several axiomatic systems that were proposed in the early twentieth century to formulate a theory of sets free of paradoxes such as Russell's paradox. Zermelo–Fraenkel set theory with the historically controversial axiom of choice included is commonly abbreviated ZFC, where C stands for choice. Many authors use ZF to refer to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded. Today ZFC is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.
has abstract
Aksjomaty Zermelo-Fraenkela, w ...... żne, otrzymuje się teorię ZFC.
@pl
Die Zermelo-Fraenkel-Mengenleh ...... also Auswahl oder Wahl steht).
@de
En lógica y matemáticas, los a ...... rías axiomáticas de conjuntos.
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En mathématiques, la théorie d ...... immédiatement à la théorie ZF.
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In de verzamelingenleer, een d ...... jke fundament van de wiskunde.
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In matematica, e in particolar ...... e AC (la "A" sta per "axiom").
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In mathematics, Zermelo–Fraenk ...... oved within the theory itself.
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Na matemática, a teoria dos co ...... dos axiomas restantes da ZFC.
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策梅洛-弗兰克尔集合论（Zermelo-Fraenkel Set Theory），含选择公理時常简写为ZFC，是在数学基础中最常用形式的公理化集合论，不含選擇公理的則簡寫為ZF。
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Wikipage page ID
Wikipage revision ID
745,042,010
id
Zermelo-FraenkelSetTheory
title
Zermelo-Fraenkel Axioms
Zermelo-Fraenkel Set Theory
hypernym
type
comment
Aksjomaty Zermelo-Fraenkela, w ...... żne, otrzymuje się teorię ZFC.
@pl
Die Zermelo-Fraenkel-Mengenleh ...... also Auswahl oder Wahl steht).
@de
En lógica y matemáticas, los a ...... n (axiom of choice), como ZFC.
@es
En mathématiques, la théorie d ...... obtenue en ajoutant celui-ci.
@fr
In de verzamelingenleer, een d ...... en die deze eigenschap hebben.
@nl
In matematica, e in particolar ...... Fraenkel, e abbreviati con ZF.
@it
In mathematics, Zermelo–Fraenk ...... mon foundation of mathematics.
@en
Na matemática, a teoria dos co ...... não urelementos (elementos de
@pt
策梅洛-弗兰克尔集合论（Zermelo-Fraenkel Set Theory），含选择公理時常简写为ZFC，是在数学基础中最常用形式的公理化集合论，不含選擇公理的則簡寫為ZF。
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label
Aksjomaty Zermelo-Fraenkela
@pl
Axiomas de Zermelo-Fraenkel
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Axiomas de Zermelo-Fraenkel
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Teoria degli insiemi di Zermelo-Fraenkel
@it
Théorie des ensembles de Zermelo-Fraenkel
@fr
Zermelo-Fraenkel-Mengenlehre
@de
Zermelo-Fraenkel-verzamelingenleer
@nl
Zermelo–Fraenkel set theory
@en
策梅洛-弗兰克尔集合论
@zh