May 2015
Szymon Żeberski: Applications of Shoenfield Absoluteness Lemma
27/05/15 21:38
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.
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.
Inna Pozdniakova: On monoids of monotone injective partial selfmaps of \(L_n\times_{\operatorname{lex}}\mathbb{Z}\) with co-finite domains and images
21/05/15 17:01
Tuesday, May 26, 2015 18:45
Room: D1-215
Speaker: Inna Pozdniakova
Title: On monoids of monotone injective partial selfmaps of \(L_n\times_{\operatorname{lex}}\mathbb{Z}\) with co-finite domains and images
Abstract. The speaker will discuss on the structure of the semigroup \(\mathscr{I\!O}\!_{\infty}(\mathbb{Z}^n_{\operatorname{lex}})\) of monotone injective partial selfmaps of the set of \(L_n\times_{\operatorname{lex}}\mathbb{Z}\) having co-finite domain and image, where \(L_n\times_{\operatorname{lex}}\mathbb{Z}\) is the lexicographic product of an \(n\)-elements chain and the set of integers with the usual order.
Room: D1-215
Speaker: Inna Pozdniakova
Title: On monoids of monotone injective partial selfmaps of \(L_n\times_{\operatorname{lex}}\mathbb{Z}\) with co-finite domains and images
Abstract. The speaker will discuss on the structure of the semigroup \(\mathscr{I\!O}\!_{\infty}(\mathbb{Z}^n_{\operatorname{lex}})\) of monotone injective partial selfmaps of the set of \(L_n\times_{\operatorname{lex}}\mathbb{Z}\) having co-finite domain and image, where \(L_n\times_{\operatorname{lex}}\mathbb{Z}\) is the lexicographic product of an \(n\)-elements chain and the set of integers with the usual order.
Taras Banakh : Separation axioms on paratopological groups and quasi-uniform spaces
20/05/15 10:19
Tuesday, May 26, 2015 17:15
Room: D1-215
Speaker: Taras Banakh
Title: Separation axioms on paratopological groups and quasi-uniform spaces
Abstract. We shall prove that each regular paratoplogical group is completely regular thus resolving an old problem in the theory of paratopological groups.
Room: D1-215
Speaker: Taras Banakh
Title: Separation axioms on paratopological groups and quasi-uniform spaces
Abstract. We shall prove that each regular paratoplogical group is completely regular thus resolving an old problem in the theory of paratopological groups.
Jarosław Swaczyna: Generalized densities of subsets of natural numbers and associated ideals
15/05/15 19:36
Tuesday, May 19, 2015 17:15
Room: D1-215
Speaker: Jarosław Swaczyna
Title: Generalized densities of subsets of natural numbers and associated ideals
Abstract. Let \(g: \omega \rightarrow [0, \infty)\). We say that \(A \subset \omega\) has \(g\)-density zero, if \(\lim_{n \rightarrow \infty} \frac{A \cap n}{g(n)} = 0\). It is an easy observation that family of \(g\)-density zero sets is an ideal.
I will discuss some properties of ideals obtained this way (among others, I will show that they can be generated using Solecki's submeasures). I will then examine inclusions between ideals obtained for different functions \(g\).
I will also discuss connections between our ideals, "density-like" ideals and Erdos-Ulam ideals. I will present joint results with M. Balcerzak, P. Das and M. Filipczak.
Room: D1-215
Speaker: Jarosław Swaczyna
Title: Generalized densities of subsets of natural numbers and associated ideals
Abstract. Let \(g: \omega \rightarrow [0, \infty)\). We say that \(A \subset \omega\) has \(g\)-density zero, if \(\lim_{n \rightarrow \infty} \frac{A \cap n}{g(n)} = 0\). It is an easy observation that family of \(g\)-density zero sets is an ideal.
I will discuss some properties of ideals obtained this way (among others, I will show that they can be generated using Solecki's submeasures). I will then examine inclusions between ideals obtained for different functions \(g\).
I will also discuss connections between our ideals, "density-like" ideals and Erdos-Ulam ideals. I will present joint results with M. Balcerzak, P. Das and M. Filipczak.
Tomasz Żuchowski: Tukey types of orthogonal ideals
08/05/15 08:24
Tuesday, May 12, 2015 17:15
Room: D1-215
Speaker: Tomasz Żuchowski
Title: Tukey types of orthogonal ideals
Abstract. A partial order \(P\) is Tukey reducible to partial order \(Q\) when there exists a function \(f:P\to Q\) such that if \(A\) is a bounded subset of \(Q\) then \(f^{-1}[A]\) is a bounded subset of \(P\). The existence of such reduction is related to some cardinal invariants of considered orders. We will show Tukey reductions between some special ideals of subsets of \(\mathbb{N}\) with the inclusion order and other partial orders.
Room: D1-215
Speaker: Tomasz Żuchowski
Title: Tukey types of orthogonal ideals
Abstract. A partial order \(P\) is Tukey reducible to partial order \(Q\) when there exists a function \(f:P\to Q\) such that if \(A\) is a bounded subset of \(Q\) then \(f^{-1}[A]\) is a bounded subset of \(P\). The existence of such reduction is related to some cardinal invariants of considered orders. We will show Tukey reductions between some special ideals of subsets of \(\mathbb{N}\) with the inclusion order and other partial orders.