Métodos de la teoría de conjuntos en la teoría de grupos infinitos abelianos

Barrera Esteban, Fernando
Montaner Frutos, Fernando (dir.) ; Bagaria i Pigrau, Joan (dir.)

Universidad de Zaragoza, CIEN, 2020
Matemáticas department, Algebra area

Máster Universitario en Modelización e Investigación Matemática, Estadística y Computación

Abstract: We see how advanced set-theoretic methods such as forcing and ultrapowers as well as large cardinals apply to the study of infinite abelian groups. A few examples in which large cardinals such as measurable, strongly compact and $\delta$-strongly compact cardinals naturally arise when dealing with infinte abelian groups are studied. In particular, we see Eda's Theorem and some results regarding the Dugas-Göbel cardinal. We also see Shelah's proof on the undecidability of the Whitehead's problem, which asks whether every Whitehead group is free. Although its restriction to groups of countable cardinality has a positive solution in ZFC, the general problem is undecidable. Indeed, both a positive and a negative answer for groups of size $\aleph_{1}$ are consistent with ZFC.

Tipo de Trabajo Académico: Trabajo Fin de Master