A Topological Approach in the Extended Fraenkel-Mostowski Model of Set Theory

Andrei Alexandru, Gabriel Ciobanu
2014 Annals of the Alexandru Ioan Cuza University - Mathematics  
Lattices of subgroups are presented as algebraic domains. Given an arbitrary group, we define the Scott topology over the subgroups lattice of that group. A basis for this topology is expressed in terms of finitely generated subgroups. Several properties of the continuous functions with respect the Scott topology are obtained; they provide new order properties of groups. Finally there are expressed several properties of the group of permutations of atoms in a permutative model of set theory. We
more » ... l of set theory. We provide new properties of the extended interchange function by presenting some topological properties of its domain. Several order and topological properties of the sets in the Fraenkel-Mostowski model remains also valid in the Extended Fraenkel-Mostowski model, even one axiom in the axiomatic description of the Extended Fraenkel-Mostowski model is weaker than its homologue in the axiomatic description of the Fraenkel-Mostowski model.
doi:10.2478/aicu-2013-0029 fatcat:fzr4ylax3ndd7lnrdkcwt74nsy