Twist-Valued Models for Three-Valued Paraconsistent Set Theory

Walter A. Carnielli, Marcelo E. Coniglio

DOI: http://dx.doi.org/10.12775/LLP.2020.015

Abstract


We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. Finally, our framework is adapted to provide a class of twist-valued models generalizing Löwe and Tarafder’s model based on logic (PS 3,∗), showing that they are paraconsistent models of ZFC. The present approach offers more options for investigating independence results in paraconsistent set theory.


Keywords


Paraconsistent set theory; Boolean-valued models; axiomatic set theory; twist structures; logics of formal inconsistency; three-valued paraconsistent logics; Leibniz’s Law

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References


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