October 2014

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

Tuesday, November 4, 2014 17:15

Room: D1-215

Speaker:
Piotr Borodulin-Nadzieja

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

Tuesday, October 28, 2014 17:15

Room: D1-215

Speaker:
Robert Rałowski

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

Tuesday, October 21, 2014 17:15

Room: D1-215

Speaker:
Marcin Michalski

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

Tuesday, October 14, 2014 17:15

Room: D1-215

Speaker:
Robert Rałowski

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

Tuesday, October 7, 2014 17:15

Room: D1-215

Speaker:
Szymon Żeberski

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: \(\mathscr{E}\), \(\mathscr{M} \cap \mathscr{N}\), \(\mathscr{M}\), \(\mathscr{N}\).