Łukasz Mazurkiewicz
Łukasz Mazurkiewicz: Analytic families of trees
22/01/24 07:12
Tuesday, January 23, 2024 17:00
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Łukasz Mazurkiewicz
Title: Analytic families of trees
Abstract: Every tree can be seen as a point in a space \(P(2^<\omega)\) or \(P(\omega^<\omega)\). Therefore, families of trees are subsets of these "incarnations" of Cantor space and, as such, can be analyzed from the perspective of descriptive complexity. In this talk I would like to explore some classical families of trees with some focus put on the ones, which are analytic complete.
Location: room 601, Mathematical Institute, University of Wroclaw
Speaker: Łukasz Mazurkiewicz
Title: Analytic families of trees
Abstract: Every tree can be seen as a point in a space \(P(2^<\omega)\) or \(P(\omega^<\omega)\). Therefore, families of trees are subsets of these "incarnations" of Cantor space and, as such, can be analyzed from the perspective of descriptive complexity. In this talk I would like to explore some classical families of trees with some focus put on the ones, which are analytic complete.
Łukasz Mazurkiewicz: Ideal analytic sets
17/01/23 09:14
Tuesday, January 17, 2023 17:00
Location: room C11-3.11
Speaker: Łukasz Mazurkiewicz
Title: Ideal analytic sets
Abstract: We will consider examples of analytic sets which are not Borel. We will focus on, so called, complete analytic sets. Firstly, we will consider ideals on naturals (naturally treated as subsets of the Cantor space). Secondly, we will consider the family of Silver trees. We will compare the later example with theorem of Kechris-Louveau-Woodin.
Location: room C11-3.11
Speaker: Łukasz Mazurkiewicz
Title: Ideal analytic sets
Abstract: We will consider examples of analytic sets which are not Borel. We will focus on, so called, complete analytic sets. Firstly, we will consider ideals on naturals (naturally treated as subsets of the Cantor space). Secondly, we will consider the family of Silver trees. We will compare the later example with theorem of Kechris-Louveau-Woodin.
Łukasz Mazurkiewicz: Possible modifications of Lusin analytic set
02/12/21 13:44
Tuesday, December 7, 2021 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Łukasz Mazurkiewicz
Title: Possible modifications of Lusin analytic set
Abstract: In the last talk we breathly mentioned an example of a complete analytic set created by Lusin. This time we will prove that it is a complete analytic set, which is not an element of \(Bor[K_\sigma]\). Then we will investigate some possible modifications of this example in order to decide, which partial orders make this set complete analytic.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Łukasz Mazurkiewicz
Title: Possible modifications of Lusin analytic set
Abstract: In the last talk we breathly mentioned an example of a complete analytic set created by Lusin. This time we will prove that it is a complete analytic set, which is not an element of \(Bor[K_\sigma]\). Then we will investigate some possible modifications of this example in order to decide, which partial orders make this set complete analytic.
Łukasz Mazurkiewicz: Families of sets closed under Suslin operation
22/11/21 13:00
Tuesday, November 23, 2021 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Łukasz Mazurkiewicz
Title: Families of sets closed under Suslin operation
Abstract: In the talk we discuss some extensions of classical results regarding closure of measurable sets and sets with Baire property under Suslin operation. This will lead us to the theory of analytic sets, where the example of an analytic set created by Lusin will be considered.
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Łukasz Mazurkiewicz
Title: Families of sets closed under Suslin operation
Abstract: In the talk we discuss some extensions of classical results regarding closure of measurable sets and sets with Baire property under Suslin operation. This will lead us to the theory of analytic sets, where the example of an analytic set created by Lusin will be considered.