Foundations of mathematics and applications

• Grant number: 11/21024-0
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: January 01, 2012
• End date: November 30, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Leandro Fiorini Aurichi
• Grantee: Hugo Rafael de Oliveira Ribeiro
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project aims to study the basic part of Mathematical Logic and Set Theory. Beside this, some other techniques of these fields will be developed looking for applications in other mathematical fields. Among such techniques are Model Theory, well order principle and extra axioms to ZFC. One of the applications is the proof of the Hilbert's Nullstellensatz using model theory. Dentre as aplicações, podemos destacar a demonstração do Teorema dos Zeros de Hilbert via Teoria dos Modelos. (AU)