Uniformly supported sets and fixed points properties

Abstract

The theory of finitely supported algebraic structures is a reformulation of Zermelo-Fraenkel set theory in which every set-based construction is finitely supported according to a canonical action of a group of permutations of some basic elements named atoms. In this paper we study the properties of finitely supported sets that contain infinite uniformly supported subsets, as well as the properties of finitely supported sets that do not contain infinite uniformly supported subsets. Particularly, we focus on fixed points properties.