Szymon Żeberski

# Szymon Żeberski: Applications of Shoenfield Absoluteness Lemma

Tuesday, June 2, 2015 17:15

Room: D1-215

Speaker:
Szymon Żeberski

Title: Applications of Shoenfield Absoluteness Lemma

Abstract. We will recall Shoenfield Absoluteness Lemma about $$\Sigma^1_2$$ sentences. We will show applications of this theorem connected to topological and algebraic structure of Polish spaces in publications co-authored by the speaker.

# Szymon Żeberski: An example of a capacity for which all positive Borel sets are thick

Tuesday, March 3, 2015 17:15

Room: D1-215

Speaker:
Szymon Żeberski

Title: An example of a capacity for which all positive Borel sets are thick

Abstract. The result is obtained together with Michał Morayne. We will show an example of a capacity on Cantors cube for which all positive Borel sets can be partitioned into continuum many positive Borel sets.

# Szymon Żeberski: $$\sigma$$-ideals invariant under measure-preserving homeomorphisms on Cantor's cube

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