Desigualdad cardinal de un espacio topológico

Ponente(s): Emmanuel Ivan Montiel Paredes, Luz María García Ávila

We study model theory, a branch of mathematical logic concerned with the relationship between a formal language and its interpretations or models. Specifically, we study elementary submodels, which have been utilized for decades, but their application in general topology has seen a notable increase over the past years. While reflection arguments appeared in works, the use of elementary submodels as a formal tool in topology was established by Alan Dow. The reseacrh develops the necessary elements of set theory and model theory to prove the existence of elementary substructures, examines the structure $H(\kappa)$, which acts as an intermediary between the universe of set theory and the elementary submodels, and provides applications of elementary submodels by proving various theorems of topological cardinal inequalities using this technique of elementary submodels.