October 2016

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

Tuesday, October 25, 2016 17:15

Room: D1-215

Speaker:
David Chodounsky

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

Tuesday, October 18, 2016 17:15

Room: D1-215

Speaker:
Marcin Michalski

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

Tuesday, October 11, 2016 17:15

Room: D1-215

Speaker:
Aleksander Cieślak

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.