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On the structure of perfect sets in various topologies associated with tree forcings

100%
Nowik A., Reardon P.
Open Mathematics
|
2013
|
tom 11
|
nr 3
509-518
EN
We prove that the Ellentuck, Hechler and dual Ellentuck topologies are perfect isomorphic to one another. This shows that the structure of perfect sets in all these spaces is the same. We prove this by finding homeomorphic embeddings of one space into a perfect subset of another. We prove also that the space corresponding to eventually different forcing cannot contain a perfect subset homeomorphic to any of the spaces above.
2
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Ordinal ultrafilters versus P-hierarchy

100%
Starosolski A.
Open Mathematics
|
2014
|
tom 12
|
nr 1
84-96
EN
An earlier paper [Starosolski A., P-hierarchy on βω, J. Symbolic Logic, 2008, 73(4), 1202–1214] investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. The present paper focuses on the aspects of characterization of classes of ultrafilters of finite index, existence, generic existence and the Rudin-Keisler-order.
3
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κ-strong sequences and the existence of generalized independent families

100%
Jureczko J.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1277-1282
EN
In this paper we will show some relations between generalized versions of strong sequences introduced by Efimov in 1965 and independent families. We also show some inequalities between cardinal invariants associated with these both notions.
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