Type: Article

Convergent sequences in iterated ultrapowers as p-compact groups

Ramos-García, Ulises Ariet; Valencia-Gómez, David;

Abstract:

Summary: "We prove, in ZFC, that if G is an infinite countable Abelian group, then there is an ultrafilter p??? such that (Ultp(G),?Bohr¯¯¯¯¯¯¯¯¯¯¯¯) has non-trivial convergent sequences, consequently (Ult?1p(G),?Bohr¯¯¯¯¯¯¯¯¯¯¯¯) has non-trivial convergent sequences, extending Theorem 3.9 from [13] [MR4196393]. In addition, we prove that the Remark 3.8 from [13] is false; so, the proof of the Corollary 3.11 is false too.''