Arbitrariness and definability in the context of non-classical logics

• Grant number: 17/23853-0
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: March 01, 2018
• End date: December 31, 2021
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Giorgio Venturi
• Grantee: Daniel Santiago Jockwich Martinez
• Host Institution: Centro de Lógica, Epistemologia e História da Ciência (CLE). 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

This project analyses the problematic relationship between arbitrary sets and the intensional notion of sets. Indeed, this distinction can be seen in the two axiomatic developments of a theory of sets as conceived on the one hand by Cantor, Dedekind and Zermelo (who stressed the arbitrariness of sets) and on the other hand by Frege and then Russell (who stressed the possibility of a restricting the existence of sets to types). In this project we plan to analyze the connection of arbitrariness and definability in a set-theoretical context, using both infinitary and paraconsistent logics. (AU)

Scientific publications

(4)

(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)

JOCKWICH MARTINEZ, S.; VENTURI, G.. On Negation for Non-classical Set Theories. JOURNAL OF PHILOSOPHICAL LOGIC, v. 50, n. 3, p. 22-pg., 2020-10-22. (17/23853-0, 16/25891-3)

MARTINEZ, SANTIAGO JOCKWICH. lgebra-valued models for LP-Set Theor. AUSTRALASIAN JOURNAL OF LOGIC, v. 18, n. 7, p. 657+, 2021. (17/23853-0)

JOCKWICH, SANTIAGO; TARAFDER, SOURAV; VENTURI, GIORGIO. Ideal Objects for Set Theory. JOURNAL OF PHILOSOPHICAL LOGIC, JAN 2022. (16/25891-3, 17/23853-0)

JOCKWICH MARTINEZ, S.; VENTURI, G.. Non-classical Models of ZF. STUDIA LOGICA, v. 109, n. 3, JUL 2020. (16/25891-3, 17/23853-0)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

MARTINEZ, Daniel Santiago Jockwich. Modelos da teoria de conjuntos não clássicas. 2021. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Filosofia e Ciências Humanas Campinas, SP.