$\in $-representation and set-prolongations
Mlček, Josef
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 661-666 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1992-01-01
Classification:  03E70,  04A99 
@article{118537,
     author = {Josef Ml\v cek},
     title = {$\in $-representation and set-prolongations},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {661-666},
     zbl = {0784.03032},
     mrnumber = {1240187},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118537}
}

Mlček, Josef. $\in $-representation and set-prolongations. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 661-666. http://gdmltest.u-ga.fr/item/118537/

Vopěnka P. Mathematics in the Alternative Set Theory, TEUBNER TEXTE Leipzig (1979). (1979) | MR 0581368