\(\in\)-representation and set-prolongations. (English) Zbl 0784.03032

The article concerns the Alternative Set Theory. An \(\in\)-representation of a relation in question is its isomorphic embedding to \(\mathbb{E}=\{\langle x,y\rangle;\;x\in y\}\). Some theorems on such a representation are presented. Especially, a version of the well-kown theorem on isomorphic representation of extensional and well-founded relations in \(\mathbb{E}\), which holds in Zermelo-Fraenkel set theory, is proved. This our version is false in ZF set theory. A general theorem on a set-prolongation is proved, too; it enables to solve the task of the representation in question.
Reviewer: J.Mlček


03E70 Nonclassical and second-order set theories
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