Introduction to Mathematical logic: an Algebraic and Topological approach

• Grant number: 12/20802-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2012
• End date: November 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Marcelo Reicher Soares
• Grantee: Vitor Tadeu Fracaroli Rocha
• Host Institution: Faculdade de Ciências (FC). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

The main purpose of the project is the study of Mathematical Logic by means of an algebraic approach. In this way, we will study Boole and Heyting algebras and we will see their connection with classic and intuitionist propositional calculus, namely, the Lindenbaum algebras. Moreover, it is our intention to investigate the proof of some interesting theorems of the theory, such as the Completeness theorems. We will also study Tarski's consequence operator, as well as its connection with Almost Topological Spaces.(AU)