Forcing, symmetric submodels and models in which AC fails

• Grant number: 21/03721-7
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2021
• End date: February 28, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Artur Hideyuki Tomita
• Grantee: Guilherme de Sousa Sobreira
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we study some applications of Forcing and methods of Symmetric Submodels on the study of consequences of the Axiom of Choice, by analyzing in details the construction of several models of ZF in which known implications of AC do not hold.