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GENERALIZED ALGEBRA-VALUED MODELS OF SET THEORY

Published online by Cambridge University Press:  12 January 2015

BENEDIKT LÖWE*
Affiliation:
Institute for Logic, Language and Computation, Universiteit van Amsterdam and Fachbereich Mathematik, Universität Hamburg
SOURAV TARAFDER*
Affiliation:
Department of Commerce (Morning), St. Xavier’s College and Department of Pure Mathematics, Calcutta University
*
*INSTITUTE FOR LOGIC, LANGUAGE AND COMPUTATION, UNIVERSITEIT VAN AMSTERDAM, POSTBUS 94242, 1090 GE AMSTERDAM, THE NETHERLANDS E-mail: b.loewe@uva.nl, FACHBEREICH MATHEMATIK, UNIVERSITÄT HAMBURG, BUNDESSTRASSE 55, 20146 HAMBURG, GERMANY
DEPARTMENT OF COMMERCE (MORNING), ST. XAVIER’S COLLEGE, 30 MOTHER TERESA SARANI, KOLKATA, 700016, INDIA E-mail: souravt09@gmail.com, DEPARTMENT OF PURE MATHEMATICS, UNIVERSITY OF CALCUTTA, 35 BALLYGUNGE CIRCULAR ROAD, KOLKATA, 700019, INDIA

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2014 

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