Back Aussonderungsaxiom German Αξιωματικό σχήμα του διαχωρισμού Greek اصل موضوع تصریح Persian Schéma d'axiomes de compréhension French Načelo komprehenzije Croatian Schema di assiomi di specificazione Italian 分出公理 Japanese Axiomaschema van afscheiding Dutch Aksjomat podzbiorów Polish Axioma da separação Portuguese
In many popular versions of axiomatic set theory, the axiom schema of specification,[1] also known as the axiom schema of separation (Aussonderungsaxiom),[2] subset axiom[3], axiom of class construction,[4] 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.[5]
- ^ "AxiomaticSetTheory". www.cs.yale.edu. Axiom Schema of Specification. Retrieved 2024-06-08.
- ^ Suppes, Patrick (1972-01-01). Axiomatic Set Theory. Courier Corporation. pp. 6, 19, 21, 237. ISBN 978-0-486-61630-8.
- ^ Cunningham, Daniel W. (2016). Set theory: a first course. Cambridge mathematical textbooks. New York, NY: Cambridge University Press. pp. 22, 24–25, 29. ISBN 978-1-107-12032-7.
- ^ Pinter, Charles C. (2014-06-01). A Book of Set Theory. Courier Corporation. p. 27. ISBN 978-0-486-79549-2.
- ^ Heinz-Dieter Ebbinghaus (2007). Ernst Zermelo: An Approach to His Life and Work. Springer Science & Business Media. p. 88. ISBN 978-3-540-49553-6.
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