Consistence and independence in definable graph combinatorics

• Grant number: 22/13561-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: April 01, 2023
• Status: Discontinued
• Field of knowledge: Physical Sciences and Mathematics - Mathematics
• Principal Investigator: Leandro Fiorini Aurichi
• Grantee: Michel Fernandes Gaspar
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 24/04155-3 - Geometric graphs and Li-Yorke systems, BE.EP.PD

Abstract

The main objective of this project is to answer set-theoretic questions about Borel and measurable colorings of graphs relevant to (1) ergodic theory; (2) hyperbolic geometry; (3) computability and (4) dynamical systems. The main technique that we may employ is iterated forcing of notions that satisfy Axiom A. If the objectives are achieved, we will have contributed to expanding the frontiers of set theory.