ZF and the axiom of choice in some paraconsistent set theories

Logic and Logical Philosophy 11:91-114 (2003)
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Abstract

In this paper, we present set theories based upon the paraconsistent logic Pac. We describe two different techniques to construct models of such set theories. The first of these is an adaptation of one used to construct classical models of positive comprehension. The properties of the models obtained in that way give rise to a natural paraconsistent set theory which is presented here. The status of the axiom of choice in that theory is also discussed. The second leads to show that any classical universe of set theory (e.g. a model of ZF) can be extended to a paraconsistent one, via a term model construction using an adapted bisimulation technique

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Citations of this work

Models for a paraconsistent set theory.Thierry Libert - 2005 - Journal of Applied Logic 3 (1):15-41.
A Strong Model of Paraconsistent Logic.Olivier Esser - 2003 - Notre Dame Journal of Formal Logic 44 (3):149-156.
Topological Models for Extensional Partial Set Theory.Roland Hinnion & Thierry Libert - 2008 - Notre Dame Journal of Formal Logic 49 (1):39-53.

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References found in this work

Natural 3-valued logics—characterization and proof theory.Arnon Avron - 1991 - Journal of Symbolic Logic 56 (1):276-294.
Paraconsistent extensional propositional logics.Diderik Batens - 1980 - Logique and Analyse 90 (90):195-234.
A note on naive set theory in ${\rm LP}$.Greg Restall - 1992 - Notre Dame Journal of Formal Logic 33 (3):422-432.
On an implication connective of RM.Arnon Avron - 1986 - Notre Dame Journal of Formal Logic 27 (2):201-209.

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