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A tree π -base for * without cofinal branches

Fernando Hernández-Hernández (2005)

Commentationes Mathematicae Universitatis Carolinae

We prove an analogue to Dordal’s result in P.L. Dordal, A model in which the base-matrix tree cannot have cofinal branches, J. Symbolic Logic 52 (1980), 651–664. He obtained a model of ZFC in which there is a tree π -base for * with no ω 2 branches yet of height ω 2 . We establish that this is also possible for * using a natural modification of Mathias forcing.

Almost maximal topologies on groups

Yevhen Zelenyuk (2016)

Fundamenta Mathematicae

Let G be a countably infinite group. We show that for every finite absolute coretract S, there is a regular left invariant topology on G whose ultrafilter semigroup is isomorphic to S. As consequences we prove that (1) there is a right maximal idempotent in βG∖G which is not strongly right maximal, and (2) for each combination of the properties of being extremally disconnected, irresolvable, and nodec, except for the combination (-,-,+), there is a corresponding regular almost maximal left invariant...

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