$\in$-representation and set-prolongations

Mlček, 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 -