000097618 001__ 97618
000097618 005__ 20210118122852.0
000097618 037__ $$aTAZ-TFM-2020-891
000097618 041__ $$aeng
000097618 1001_ $$aBarrera Esteban, Fernando
000097618 24200 $$aSet-theoretic methods in infinite abelian group theory
000097618 24500 $$aMétodos de la teoría de conjuntos en la teoría de grupos infinitos abelianos
000097618 260__ $$aZaragoza$$bUniversidad de Zaragoza$$c2020
000097618 506__ $$aby-nc-sa$$bCreative Commons$$c3.0$$uhttp://creativecommons.org/licenses/by-nc-sa/3.0/
000097618 520__ $$aWe see how advanced set-theoretic methods such as forcing and ultrapowers as well as large cardinals apply to the study of infinite abelian groups. A few examples in which large cardinals such as measurable, strongly compact and $\delta$-strongly compact cardinals naturally arise when dealing with infinte abelian groups are studied. In particular, we see Eda's Theorem and some results regarding the Dugas-Göbel cardinal. We also see Shelah's proof on the undecidability of the Whitehead's problem, which asks whether every Whitehead group is free. Although its restriction to groups of countable cardinality has a positive solution in ZFC, the general problem is undecidable. Indeed, both a positive and a negative answer for groups of size $\aleph_{1}$ are consistent with ZFC. <br /><br />
000097618 521__ $$aMáster Universitario en Modelización e Investigación Matemática, Estadística y Computación
000097618 540__ $$aDerechos regulados por licencia Creative Commons
000097618 700__ $$aMontaner Frutos, Fernando$$edir.
000097618 700__ $$aBagaria i Pigrau, Joan$$edir.
000097618 7102_ $$aUniversidad de Zaragoza$$bMatemáticas$$cAlgebra
000097618 8560_ $$f659249@unizar.es
000097618 8564_ $$s713615$$uhttps://zaguan.unizar.es/record/97618/files/TAZ-TFM-2020-891.pdf$$yMemoria (eng)
000097618 909CO $$ooai:zaguan.unizar.es:97618$$pdriver$$ptrabajos-fin-master
000097618 950__ $$a
000097618 951__ $$adeposita:2021-01-18
000097618 980__ $$aTAZ$$bTFM$$cCIEN
000097618 999__ $$a20200908234322.CREATION_DATE