A logical analysis of the notion of consistency in set theoretical practice
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Grant number: | 13/25095-4 |
Support type: | Scholarships in Brazil - Post-Doctorate |
Effective date (Start): | March 01, 2014 |
Effective date (End): | February 13, 2017 |
Field of knowledge: | Humanities - Philosophy - Logic |
Principal researcher: | Walter Alexandre Carnielli |
Grantee: | Giorgio Venturi |
Home Institution: | Centro de Lógica, Epistemologia e História da Ciência (CLE). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil |
Associated research grant: | 10/51038-0 - Logical consequence, reasoning and computation - LOGCONS, AP.TEM |
Associated scholarship(s): | 14/25342-4 - A logical analysis of the notion of consistency in set theoretical practice, BE.EP.PD |
Abstract With this project I propose to investigate the phenomenon of independence in set theory in the context of paraconsistent logic, by a multidisciplinary point of view. The main motivation of this work comes from the limits of classical logic in the study of the notion of truth in the models of ZFC (i.e the standard first order axiomatization of set theory). In particular I plan to apply a Logic of Formal Inconsistency (LFI) in the study of the mathematical structure that consists of all possible models that we can obtain by means of the method of forcing (the multiverse). The first goal is to determine which are the best paraconistent logical principles that can describe the multiverse, while the second - and main - goal is to determine if and how it is possible to perform independence proofs in a paraconsitent set theory (i.e. a set theory whose internal logic is paraconsitent; in particular an LFI). In particular I plan to define and to study a paraconsistent version of the constructible class $L$ and a paraconsistent version of the method of forcing. Besides, my research project aims to give a philosophical justification of the use of a paraconsistent logic in the study of independence in set theory, discussing its quasi-empirical character and the consequences that this aspect has on the notion of truth in set theory. | |
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