# Article

 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: http://hdl.handle.net/10338.dmlcz/118537 . Reference: [V] Vopěnka P.: Mathematics in the Alternative Set Theory.TEUBNER TEXTE Leipzig (1979). MR 0581368 .

## Files

Files Size Format View
CommentatMathUnivCarolRetro_33-1992-4_11.pdf 186.4Kb application/pdf View/Open

Partner of