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Algebra-valued models of non-classical set theories

Grant number: 19/12527-0
Support type:Research Grants - Visiting Researcher Grant - International
Duration: October 16, 2019 - October 15, 2020
Field of knowledge:Humanities - Philosophy
Principal Investigator:Giorgio Venturi
Grantee:Giorgio Venturi
Visiting researcher: Sourav Tarafder
Visiting researcher institution: St. Xavier's College (SXC), India
Home Institution: Instituto de Filosofia e Ciências Humanas (IFCH). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated research grant:16/25891-3 - Arbitrariness and genericity: or on how to speak of the unspeakable, AP.JP


We intend to develop the theory of models of non-classical set theories, in particular, paraconsistent set theories. In previous work, the visiting researcher developed a paraconsistent model of set theory in which the negation-free fragment of ZF is valid, but which does not satisfy Leibniz's law of indiscernibility of identicals. In this project, we aim to improve on these results by finding non-classical models which validate larger fragments of ZF, as well as studying the relationship between paraconsistency and Leibniz's law in these models (Aim A). Based on these models, we shall then study notions of ordinals and cardinals (Aim B) as well as the basic analytic and algebraic notions of topological spaces, metric spaces, groups, vector spaces etc. (Aim C). (AU)