Introduction to first order theories

• Grant number: 19/25956-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2020
• End date: September 28, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Fabio Ferrari Ruffino
• Grantee: Guilherme Marques Sonoda
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The main aim of this project consists in introducing the candidate to the fundamental notions of mathematical logic. In particular, he will begin by deepening his knowledge on naive set theory, dealing with von Neumann theory of ordinals and cardinals and with the class of well-founded sets. Afterwards, he will study in detail propositional calculus and first-order theories, both from syntactic and semantic point of view. The project will be concluded ``formalizing'' naive set theory through Zermelo-Fraenkel axioms. (AU)