Permutative Renamings in the Extended Fraenkel-Mostowski Set Theory

Abstract

In the new framework of the extended Fraenkel-Mostowski set theory, we define an extended interchange function as an action on a permutation group, and a new notion of permutative renaming by generalizing an existing notion of finitary permutative renaming. Some algebraic and combinatorial properties of permutative renamings expressed by using the Fraenkel-Mostowski axioms remain valid in the new framework even if we replace one axiom with a weaker axiom.