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Title: $\in $-representation and set-prolongations (English)
Author: Mlček, Josef
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 33
Issue: 4
Year: 1992
Pages: 661-666
Category: math
Summary: By an $\in $-representation of a relation we mean its isomorphic embedding to $\Bbb E = \{\langle x,y\rangle;\,x\in y\}$. Some theorems on such a representation are presented. Especially, we prove a version of the well-known theorem on isomorphic representation of extensional and well-founded relations in $\Bbb E$, which holds in Zermelo-Fraenkel set theory. This our version is in Zermelo-Fraenkel set theory false. A general theorem on a set-prolongation is proved; it enables us to solve the task of the representation in question. (English)
Keyword: isomorphic representation
Keyword: extensional relation
Keyword: well-founded relation
Keyword: set-pro\-lon\-gation
MSC: 03E70
MSC: 04A99
idZBL: Zbl 0784.03032
idMR: MR1240187
Date available: 2009-01-08T17:59:30Z
Last updated: 2012-04-30
Stable URL:
Reference: [V] Vopěnka P.: Mathematics in the Alternative Set Theory.TEUBNER TEXTE Leipzig (1979). MR 0581368


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