Seminario Teoría de grupos UAM-ICMAT

Jueves, 17 de Mayo, Aula 520 (UAM), 15:00

Ponente: Sam Corson (UPV/EHU)

Título: The price of freedom

Abstract:  "The axiom of choice has been a useful tool in understanding uncountable groups.  It is used in producing nonconstructive homomorphisms, selecting Hamel bases, and determining the freeness of certain groups.  We explore algebraic consequences that  hold under an alternative to this axiom. Certain algebraic structures will lack freeness.  These include some subgroups of the Baer-Specker group $mathbb{Z}^{omega}$ and of the Hawaiian earring group.  Selection of bases for certain vector spaces is also impossible.  Applications to slenderness, completely metrizable topological groups, length functions and strongly bounded groups will also be discussed.

The work presented is joint with Saharon Shelah.