October 2014

# Piotr Borodulin-Nadzieja: Analytic P-ideals and Banach spaces

30/10/14 19:44

Tuesday, November 4, 2014 17:15

*Room:*D1-215*Piotr Borodulin-Nadzieja*

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*Title*: Analytic P-ideals and Banach spaces*Abstract*. We consider certain generalization of the notion of summability of an ideal (on the natural numbers) which connects theory of analytic P-ideals with the theory of Banach spaces.# Robert Rałowski: On m.a.d. \(s_0\)-nonmeasurable sets with a small dominating subfamilies

27/10/14 16:02

Tuesday, October 28, 2014 17:15

*Room:*D1-215*Robert Rałowski*

Speaker:Speaker:

*Title*: On m.a.d. \(s_0\)-nonmeasurable sets with a small dominating subfamilies*Abstract*. We show that \(\mathfrak{d}=\aleph_1\) implies the existence of maximal familiy of eventually different reals on Baire space which forms a nonmeasurable set with respect to an ideals generated by trees (perfect, Laver or Miller trees for example).# Marcin Michalski: Luzin and Sierpiński sets, some nonmeasurable subsets of the plane

16/10/14 19:06

Tuesday, October 21, 2014 17:15

*Room:*D1-215*Marcin Michalski*

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*Title:*Luzin and Sierpiński sets, some nonmeasurable subsets of the plane*Abstract:*We shall introduce some nonmeasurable and completely nonmeasurable subsets of the plane with various additional properties, e.g. being Hamel basis, intersecting each line in a strong Luzin/Sierpiński set. Also some additive properties of Luzin and Sierpiński sets and their generalization, \(\mathcal{I}\)-Luzin sets, on the line are investigated.# Robert Rałowski: Nonmeasurability with respect to Marczewski ideal

09/10/14 17:51

Tuesday, October 14, 2014 17:15

*Room:*D1-215*Robert Rałowski*

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*Title:*Nonmeasurability with respect to Marczewski ideal*Abstract:*Among the others we show relative consistency of ZFC theory with \(\aleph_1< 2^{\aleph_0}\) and there is a nonmesurable (with respect to ideal generated by complete Laver trees) m.a.d. family \(\mathcal{A}\) on Baire space \(\omega^\omega\). In ZFC there is a subset \(\mathcal{A}’\subseteq \mathcal{A}\) of size \(\aleph_1\) unbounded in \(\omega^\omega\). We show that there is m.a.d. family which is nonmeasurable with respect to Marczewski ideal.# Szymon Żeberski: \(\sigma\)-ideals invariant under measure-preserving homeomorphisms on Cantor's cube

02/10/14 21:07

Tuesday, October 7, 2014 17:15

*Room:*D1-215*Szymon Żeberski*

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*Title:*\(\sigma\)-ideals invariant under measure-preserving homeomorphisms on Cantor's cube*Abstract:*Results were obtained together with Taras Banakh and Robert Rałowski. We will show that there are only four nontrivial sigma-ideals with Borel base invariant under measure preserving homeomorphisms on Cantor's cube. These ideals are: \(\mathscr{E}\), \(\mathscr{M} \cap \mathscr{N}\), \(\mathscr{M}\), \(\mathscr{N}\).