Marcin Michalski: On some properties of sigma-ideals

Tuesday, October 18, 2016, 17:15
Wrocław University of Technology, 215 D-1

Speaker: Marcin Michalski (Wrocław University of Science and Technology)

Title: On some properties of sigma-ideals


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.

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