par Esser, Olivier 
Référence Mathematical logic quarterly, 45, 1, page (105-116)
Publication Publié, 1999
Référence Mathematical logic quarterly, 45, 1, page (105-116)
Publication Publié, 1999
Article révisé par les pairs
| Résumé : | In positive theories, we have an axiom scheme of comprehension for positive formulas. We study here the "generalized positive" theory GPK+∞. Natural models of this theory are hyperuniverses. The author has shown in [2] that GPK+∞ interpretes the Kelley-Morse class theory. Here we prove that GPK+∞ + ACWF (ACWF being a form of the axiom of choice allowing to choose elements in well-founded sets) and the Kelley-Morse class theory with the axiom of global choice and the axiom "On is ramifiable" are mutually interpretable. This shows that GPK+∞ + ACWF is a "strong" theory since "On is ramifiable" implies the existence of a proper class of inaccessible cardinals. |
