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$\in$ -representation and set-prolongations

Josef Mlček (1992)

Commentationes Mathematicae Universitatis Carolinae

By an $\in$ -representation of a relation we mean its isomorphic embedding to $𝔼 = {〈 x, y 〉; x \in y}$ . 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 $𝔼$ , 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.

In this paper we sketch the development and give a model of the formal version of a generalization of the Alternative Set Theory.

Currently displaying 1 – 20 of 130

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Displaying 1 – 20 of 130

$\in$ -representation and set-prolongations

A contribution to topology in AST: Almost indiscernibilities

A contribution to topology in AST: Compactness

A Hamiltonian property of connected sets in the alternative set theory.

A method for constructing some endomorphic universes

A nonstandard set theory

A nonstandard treatment with quantities

A notion of measure for classes in AST

A sequential approach to a construction of measures

A theorem on supports in the theory of semisets

Addition of initial segments. I.

Addition of initial segments. II.

Algebraic models of intuitionistic theories of sets and classes.

Alternative set theory with elementary classes

An elimination of infinitely small quantities and infinitely large numbers (within the framework of AST)

An elimination of the predicate “to be a standard member” in nonstandard models of arithmetic

Analyse relative

Approximations of $σ$ -classes and $π$ -classes

Archimedean and geodetical biequivalences

Arithmetic of cuts and cuts of classes

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