Superinductive classes in class-set theory.

Superinductive classes in class-set theory

Alternative set theory with elementary classes

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

Some Classes of Associative Binary Operations in Fuzzy Set Theory

The main aim of this paper is to summarize recent advances on some new classes of associative operations (uninorms, nullnorms, t-operators) used in fuzzy set theory.

Notions of symmetry n set theory with classes

We adapt C. Freiling’s axioms of symmetry [5] to models of set theory with classes by identifying small classes with sets getting thus a sequence of principles An, for n ≥ 2, of increasing strength. Several equivalents of A2 are given. A2 is incompatible both with the foundation axiom and the antifoundation axioms AFA∼ considered in [1]. A hierarchy of symmetry degrees of preorderings (and of c...

The Formulae-as-Classes Interpretation of Constructive Set Theory

The main objective of this paper is to show that a certain formulae-asclasses interpretation based on generalized set recursive functions provides a selfvalidating semantics for Constructive Zermelo-Fraenkel Set theory, CZF. It is argued that this interpretation plays a similar role for CZF as the constructible hierarchy for classical set theory, in that it can be employed to show that CZF is e...