Abstract
In this paper we present a new axiomatic model of set theory called the Extended Fraenkel Mostowski model. It is dened by replacing an axiom of the Fraenkel- Mostowski model with a consequence of it; the other axioms of the Fraenkel-Mostowski model are left unchanged in the new Extended Fraenkel-Mostowski model. We use the theory of groups to dene the sets both in the Extended Fraenkel- Mostowski and in the Fraenkel-Mostowski approach. Several algebraic properties of the sets in the Fraenkel-Mostowski model remain 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. Mathematics Subject Classication
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