Notions of symmetry in set theory with classes

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...

Terminal notions in set theory

Certain set theoretical notions cannot be split into finer subnotions.

Symmetry classes of polynomials associated with the dihedral group

‎In this paper‎, ‎we obtain the dimensions of symmetry classes of polynomials associated with‎ ‎the irreducible characters of the dihedral group as a subgroup of‎ ‎the full symmetric group‎. ‎Then we discuss the existence of o-basis‎ ‎of these classes‎.

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.

Superinductive classes in class-set theory