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An interpretation of the Zermelo-Fraenkel set theory and the Kelley-Morse set theory in a positive theory

par Esser, Olivier
Référence Mathematical logic quarterly, 43, 3, page (369-377)
Publication Publié, 1997

Article révisé par les pairs

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Résumé :

An interesting positive theory is the GPK theory. The models of this theory include all hyperuniverses (see [5] for a definition of these ones). Here we add a form of the axiom of infinity and a new scheme to obtain GPK+∞. We show that in these conditions, we can interprete the Kelley-Morse theory (KM) in GPK+∞, (Theorem 3.7). This needs a preliminary property which give an interpretation of the Zermelo-Fraenkel set theory (ZF) in GPK+∞. We also see what happens in the original GPK theory. Before doing this, we first need to study the basic properties of the theory. This is done in the first two sections.