# $\in $-representation and set-prolongations

Commentationes Mathematicae Universitatis Carolinae (1992)

- Volume: 33, Issue: 4, page 661-666
- ISSN: 0010-2628

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topMlček, Josef. "$\in $-representation and set-prolongations." Commentationes Mathematicae Universitatis Carolinae 33.4 (1992): 661-666. <http://eudml.org/doc/247407>.

@article{Mlček1992,

abstract = {By an $\in $-representation of a relation we mean its isomorphic embedding to $\mathbb \{E\} = \lbrace \langle x,y\rangle ;\,x\in y\rbrace $. 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 $\mathbb \{E\}$, 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.},

author = {Mlček, Josef},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {isomorphic representation; extensional relation; well-founded relation; set-prolongation; extensional, well-founded relation; Alternative Set Theory; isomorphic representation; set-prolongation},

language = {eng},

number = {4},

pages = {661-666},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {$\in $-representation and set-prolongations},

url = {http://eudml.org/doc/247407},

volume = {33},

year = {1992},

}

TY - JOUR

AU - Mlček, Josef

TI - $\in $-representation and set-prolongations

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 1992

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 33

IS - 4

SP - 661

EP - 666

AB - By an $\in $-representation of a relation we mean its isomorphic embedding to $\mathbb {E} = \lbrace \langle x,y\rangle ;\,x\in y\rbrace $. 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 $\mathbb {E}$, 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.

LA - eng

KW - isomorphic representation; extensional relation; well-founded relation; set-prolongation; extensional, well-founded relation; Alternative Set Theory; isomorphic representation; set-prolongation

UR - http://eudml.org/doc/247407

ER -

## References

top- Vopěnka P., Mathematics in the Alternative Set Theory, TEUBNER TEXTE Leipzig (1979). (1979) MR0581368

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