Some techniques and applications of Model Theory

• Grant number: 18/24490-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2019
• End date: November 22, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Leandro Fiorini Aurichi
• Grantee: Henrique de Almeida Lecco
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Model Theory refers to the study of mathematical structures, such as groups, fields, orders and graphs, under a logical approach, therefore, in a manner of foundations. Those structures are built from a language, which contains logical and non-logical symbols, and theories,\text it{i.e.} sets of sentences. Besides the importance of Model Theory as a self-contained field, it is necessary to point out the great possibility of application in other fields, such as Analysis, Algebra, Topology and even Theoretical Computer Science. This project aims to study some topics in Model Theory, as well as some of its applications.