Archive for Mathematical Logic 50 (3-4):411-421 (2011)

We prove that if an ultrafilter ${\mathcal{L}}$ is not coherent to a Q-point, then each analytic non-σ-bounded topological group G admits an increasing chain ${\langle G_\alpha:\alpha < \mathfrak b(\mathcal L)\rangle}$ of its proper subgroups such that: (i) ${\bigcup_{\alpha}G_\alpha=G}$ ; and (ii) For every σ-bounded subgroup H of G there exists α such that ${H\subset G_\alpha}$ . In case of the group Sym(ω) of all permutations of ω with the topology inherited from ω ω this improves upon earlier results of S. Thomas
Keywords Q-points   P κ -point   σ-bounded group   ω-bounded group  Menger property   $${[\mathcal{F}]}$$ -Menger property
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DOI 10.1007/s00153-010-0222-7
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References found in this work BETA

Special ultrafilters and cofinal subsets of $$({}^omega omega, <^*)$$.Peter Nyikos - 2020 - Archive for Mathematical Logic 59 (7-8):1009-1026.
Near Coherence of Filters. I. Cofinal Equivalence of Models of Arithmetic.Andreas Blass - 1986 - Notre Dame Journal of Formal Logic 27 (4):579-591.
Groupwise Density and the Cofinality of the Infinite Symmetric Group.Simon Thomas - 1998 - Archive for Mathematical Logic 37 (7):483-493.
On the Cofinality of Ultrapowers.Andreas Blass & Heike Mildenberger - 1999 - Journal of Symbolic Logic 64 (2):727-736.

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