Abstract: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.
Keywords: isomorphic representation, extensional relation, well-founded relation, set-prolongation
AMS Subject Classification: 03E70, 04A99