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On some ideal related to the ideal (v0)

100%
Kalemba P.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
The ideal (v0) is known in the literature and is naturally linked to the structure [ω]ω. We consider some natural counterpart of the ideal (v0) related in an analogous way to the structure Dense(ℚ) and investigate its combinatorial properties. By the use of the notion of ideal type we prove that under CH this ideal is isomorphic to (v0).
2
Content available remote

Universally Kuratowski–Ulam Spaces And Open-Open Games

63%
Kalemba P., Kucharski A.
Annales Mathematicae Silesianae
|
2015
|
tom 29
|
nr 1
85-92
EN
We examine the class of spaces in which the second player has a winning strategy in the open-open game. We show that this spaces are not universally Kuratowski–Ulam. We also show that the games G and G7 introduced by P. Daniels, K. Kunen, H. Zhou [Fund. Math. 145 (1994), no. 3, 205–220] are not equivalent.
3
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Ideals which generalize (v 0)

63%
Kalemba P., Plewik S.
Open Mathematics
|
2010
|
tom 8
|
nr 6
1016-1025
EN
Countable products of finite discrete spaces with more than one point and ideals generated by Marczewski-Burstin bases (assigned to trimmed trees) are examined, using machinery of base tree in the sense of B. Balcar and P. Simon. Applying Kulpa-Szymanski Theorem, we prove that the covering number equals to the additivity or the additivity plus for each of the ideals considered.
4
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On the ideal (v 0)

51%
Kalemba P., Plewik S., Wojciechowska A.
Open Mathematics
|
2008
|
tom 6
|
nr 2
218-227
EN
The σ-ideal (v 0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see [9]. We introduce segment topologies to state some resemblances of (v 0) to the family of Ramsey null sets. To describe add(v 0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v 0) = add(v 0) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v 0) = ω 1 implies that (v 0) has the ideal type (c, ω 1, c).
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