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Inconsistency of the Axiom of Choice with the Positive Theory $GPK^+ \infty$
Journal of Symbolic Logic 65 (4):1911-1916 (2000)
Abstract
The idea of the positive theory is to avoid the Russell's paradox by postulating an axiom scheme of comprehension for formulas without "too much" negations. In this paper, we show that the axiom of choice is inconsistent with the positive theory $GPK^+ \infty$Links
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Citations of this work
ZF and the axiom of choice in some paraconsistent set theories.Thierry Libert - 2003 - Logic and Logical Philosophy 11:91-114.
About the coexistence of “classical sets” with “non-classical” ones: A survey.Roland Hinnion - 2003 - Logic and Logical Philosophy 11:79-90.
References found in this work
On the Consistency of a Positive Theory.Olivier Esser - 1999 - Mathematical Logic Quarterly 45 (1):105-116.
Choice principles in hyperuniverses.Marco Forti & Furio Honsell - 1996 - Annals of Pure and Applied Logic 77 (1):35-52.
An Interpretation of the Zermelo‐Fraenkel Set Theory and the Kelley‐Morse Set Theory in a Positive Theory.Olivier Esser - 1997 - Mathematical Logic Quarterly 43 (3):369-377.
Addendum and corrigendum Choice Principles in Hyperuniverses Annals of Pure and Applied Logic 77 (1996) 35–52.Marco Forti & Furio Honsell - 1998 - Annals of Pure and Applied Logic 92 (2):211-214.
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