Uniformly supported sets and fixed points properties

DOI: https://doi.org/10.37193/CJM.2020.03.03

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.