Forcing a classification of non-torsion Abelian groups of size at most \(2^\mathfrak c\) with non-trivial convergent sequences

We force a classification of all the Abelian groups of cardinality at most \(2^\mathfrak c\) that admit a countably compact group with a non-trivial convergent sequence. In particular, we answer (consistently) Question 24 of Dikranjan and Shakhmatov for cardinality at most \(2^{\mathfrak c}\), by sh...

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Bibliographic Details
Published inarXiv.org
Main Authors Bellini, Matheus Koveroff, de Oliveira Rodrigues, Vinicius, Tomita, Artur Hideyuki
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 17.06.2020
Subjects
Classification
Convergence
Group theory
Topology
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Summary:We force a classification of all the Abelian groups of cardinality at most \(2^\mathfrak c\) that admit a countably compact group with a non-trivial convergent sequence. In particular, we answer (consistently) Question 24 of Dikranjan and Shakhmatov for cardinality at most \(2^{\mathfrak c}\), by showing that if a non-torsion Abelian group of size at most \(2^\mathfrak c\) admits a countably compact Hausdorff group topology, then it admits a countably compact Hausdorff group topology with non-trivial convergent sequences.
ISSN:2331-8422