Open Coloring Axiom and other coloring applications

• Grant number: 21/02478-1
• Support Opportunities: Scholarships in Brazil - Master
• Start date: August 01, 2021
• End date: April 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Leandro Fiorini Aurichi
• Grantee: Thales Sarinho Galvão Santos de Souza
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

The Open Coloring Axiom (OCA) is an axiom in set theory that is not a ZFC axiom. Its study involves several applications in a various contexts, among them, it is possible to mention studies regarding the consistency of OCA with the ZFC axioms, results about subsets of the real line (which can be generalized to separable metric spaces) and Boolean algebras. Furthermore, it is an objective of this project to study colorations in various contexts such as graphs obtained from elements of the real line, Ramsey theorems and its applications. This project aims at, especially, the aspects described above, besides the study of set theoretic techniques as well as combinatorics techniques needed in the mentioned contexts. (AU)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

SOUZA, Thales Sarinho Galvão Santos de. Open Coloring Axiom and coloring applications. 2023. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.