Marcin Michalski: On some properties of sigma-ideals
17/10/16 22:50
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.
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.