Algebra-valued models of non-classical set theories

• Grant number: 19/12527-0
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: October 16, 2019
• End date: October 15, 2020
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Giorgio Venturi
• Grantee: Giorgio Venturi
• Visiting researcher: Sourav Tarafder
• Visiting researcher institution: St. Xavier's College (SXC), India
• Host 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

Abstract

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)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

TARAFDER, SOURAV; VENTURI, GIORGIO. ZF Between Classicality and Non-classicality. STUDIA LOGICA, v. 110, n. 1, AUG 2021. (16/25891-3, 19/12527-0)