Generalized Algebra-Valued Models of Set Theory

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Review of Symbolic Logic 8 (1):192-205 (2015)
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Abstract

We generalize the construction of lattice-valued models of set theory due to Takeuti, Titani, Kozawa and Ozawa to a wider class of algebras and show that this yields a model of a paraconsistent logic that validates all axioms of the negation-free fragment of Zermelo-Fraenkel set theory.

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10.1017/s175502031400046x

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Benedikt Löwe
University of Amsterdam

Citations of this work

Paraconsistent logic.Graham Priest - 2008 - Stanford Encyclopedia of Philosophy.
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Independence Proofs in Non-Classical Set Theories.Sourav Tarafder & Giorgio Venturi - 2023 - Review of Symbolic Logic 16 (4):979-1010.
Non-classical Models of ZF.S. Jockwich Martinez & G. Venturi - 2020 - Studia Logica 109 (3):509-537.

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References found in this work

Transfinite numbers in paraconsistent set theory.Zach Weber - 2010 - Review of Symbolic Logic 3 (1):71-92.
A note on naive set theory in ${\rm LP}$.Greg Restall - 1992 - Notre Dame Journal of Formal Logic 33 (3):422-432.

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