Models for da Costa’s paraconsistent set theory

• Aldo Figallo-Orellano UNICAMP http://orcid.org/0000-0001-5844-3371
• Juan Sebastián Slagter Universidad Nacional del Sul http://orcid.org/0000-0002-3440-9264

DOI: https://doi.org/10.5753/wbl.2020.11456

Resumo

In this work we will be constructed F-structures-valued models as generalization of Boolean-valued models and proved that these models that verify Leibniz’ Law validate all the set-theoretic axioms of da Costa’s Paraconsistent Set Theory type ZF.

Palavras-chave: Paraconsistence, Set theory, Leibniz’ law

Referências

Bell, J. (2005). Set theory. boolean valued models and independence proofs. Oxford Science Pubblications.

Bell, J. (2014). Intuitionistic set theory. College Publications.

da Costa, N. (1963). Sistemas formais inconsistentes. Habilitation thesis. Habilitation thesis, Universidade Federal do Paraná, Curitiba, Brazil.

Fidel, M. (1977). The decidability of the calculi C n . Reports on Mathematical Logic, pages 31–40.

Löwe, B. and Tarafder, S. (2015). Generalized algebra-valued models of set theory. Re- view of Symbolic Logic. 8(1), 192–205.

H. Rasiowa (1974) An algebraic approach to non-clasical logics, Studies in logic and the foundations of mathematics, vol. 78. North-Holland Publishing Company, Amsterdam and London, and American Elsevier Publishing Company, Inc., New York.