A new conception of abstract logic as base for definability theory

• Grant number: 21/12772-4
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: April 01, 2022
• End date: June 05, 2023
• Field of knowledge: Humanities - Philosophy - Logic
• Principal Investigator: Edelcio Gonçalves de Souza
• Grantee: Luiza Silva Porto Ramos
• Host Institution: Faculdade de Filosofia, Letras e Ciências Humanas (FFLCH). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The aim of this project is to develop a unified framework for logic systems based on the Fräissé method for first order logic. Our purpose is to provide a more refined treatment to the notion of definability which can be applied to compare expressive power of logic systems. Briefly, we shall (i) to develop proper definition of logic system based on definability and contrast it to to others well known approaches to abstract logic; (ii) to transpose results of first order definability theory, in both finite and infinite aspects, to our unified context; (iii) to investigate the relevance of this context to the foundations of mathematics.