On the Consistency of a Positive Theory

Mathematical Logic Quarterly 45 (1):105-116 (1999)
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Abstract

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∞+ interprets the Kelley Morse class theory. Here we prove that GPK∞+ + ACWF 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

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References found in this work

The consistency problem for positive comprehension principles.M. Forti & R. Hinnion - 1989 - Journal of Symbolic Logic 54 (4):1401-1418.
Choice principles in hyperuniverses.Marco Forti & Furio Honsell - 1996 - Annals of Pure and Applied Logic 77 (1):35-52.
Inconsistency of GPK + AFA.Olivier Esser - 1996 - Mathematical Logic Quarterly 42 (1):104-108.

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