Small cardinals: consistency and applications to topology

• Grant number: 15/20020-1
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2015
• End date: September 30, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Cristóbal Rodríguez Porras
• Grantee: Fernando Augusto Joaquim
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project we will study the so called small cardinals: their various definitions, the relations between them which can be proven in ZFC, some which are consistent with ZFC and some applications to Topology. The main references are the recently published book [2] and the more traditional paper [3]. The student has already obtained the background in topology and set theory which is needed to work on this project.