October 2016

# David Chodounsky: Combinatorial properties of the Mathias-Prikry forcing

20/10/16 09:19

Tuesday, October 25, 2016 17:15

*Room:*D1-215*David Chodounsky*

Speaker:Speaker:

*Title*: Combinatorial properties of the Mathias-Prikry forcing*Abstract*. I will review basic fact and results about the Mathias-Prikry forcing and I will present and prove sufficient condition for genericity of reals with respect to this poset. Time permitting, further connections of parameters of the forcing with its properties will be explored.# Marcin Michalski: On some properties of sigma-ideals

17/10/16 22:50

Tuesday, October 18, 2016 17:15

*Room:*D1-215*Marcin Michalski*

Speaker:Speaker:

*Title*: On some properties of sigma-ideals*Abstract*. We shall consider a couple of properties of \(\sigma\)-ideals and relations between them. Namely we will prove that \(\mathfrak c\)-cc \(\sigma\)-ideals are tall, Weaker Smital Property implies that every Borel \(\mathcal{I}\)-positive set contains a witness for non(\(\mathcal{I}\)) as well, as satisfying ccc and Fubini Property. We give also a characterization of nonmeasurability of \(\mathcal{I}\)-Luzin sets and prove that the ideal \([\mathbb R]^{\leq\omega}\) does not posses the Fubini Property using some interesting lemma about perfect sets.# Aleksander Cieślak: Nonmeasurable images in Polish space with respect to selected sigma ideals

10/10/16 11:06

Tuesday, October 11, 2016 17:15

*Room:*D1-215*Aleksander Cieślak*

Speaker:Speaker:

*Title*: Nonmeasurable images in Polish space with respect to selected sigma ideals*Abstract*. We present results on nonmeasurability (with respect to a selected σ-ideal on a Polish space) of images of functions defined on Poilish spaces. In particular, we give a positive answer to the following question: Is there a subset of the unit disc in the real plane such that continuum many projections onto lines are Lebesgue measurable and continuum many projections are not? Results were obtained together with Robert Rałowski.