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Convergent sequences in iterated ultrapowers as \(p\)-compact groups - MaRDI portal

Convergent sequences in iterated ultrapowers as \(p\)-compact groups (Q6545211)

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scientific article; zbMATH DE number 7854787
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Convergent sequences in iterated ultrapowers as \(p\)-compact groups
scientific article; zbMATH DE number 7854787

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    Convergent sequences in iterated ultrapowers as \(p\)-compact groups (English)
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    29 May 2024
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    Let \(G\) be an infinite countable abelian group. The main result of the paper states that, in the framework of ZFC, there exists a non-principal ultrafilter \(p\) on \(\omega\) such that the topological group \(\left(\mathrm{Ult}_p(G),\tau_{\overline{Bohr}}\right)\) has non-trivial convergent sequences. Furthermore, the authors identify some errors in the paper ``Countably compact groups without non-trivial convergent sequences'' by \textit{M. Hrušák} et al. [Trans. Am. Math. Soc. 374, No. 2, 1277--1296 (2021; Zbl 1482.22002)].
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    \(p\)-compact groups
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    ultrapowers
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    countably compact groups without convergent sequences
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