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.

Tags: Piotr Borodulin-Nadzieja

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 $\mathfrak{d}={\mathrm{\aleph }}_1$ 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).

Tags: Robert Rałowski

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.

Tags: Marcin Michalski

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 ${\mathrm{\aleph }}_1<2^{{\mathrm{\aleph }}_0}$ 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 ${\mathcal{A}}^{\prime }\subseteq \mathcal{A}$ of size ${\mathrm{\aleph }}_1$ unbounded in ${\omega }^{\omega }$. We show that there is m.a.d. family which is  nonmeasurable with respect to Marczewski ideal.

Tags: Robert Rałowski

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: $\mathcal{E}$, $\mathcal{M}\cap \mathcal{N}$, $\mathcal{M}$, $\mathcal{N}$.

Tags: Szymon Żeberski