Rafał Filipów
Rafał Filipów: Does there exist a Hindman space which is not a van der Waerden space?
30/05/22 09:19
Tuesday, May 31, 2022 17:00
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Rafał Filipów (University of Gdańsk)
Title: Does there exist a Hindman space which is not a van der Waerden space?
Abstract: Both Hindman spaces and van der Waerden spaces were defined by M. Kojman (Proc. AMS 130(2002), no. 3 and no. 6) with the aid of Hindman's finite sum theorem and van der Waerden's theorem on arithmetic progressions, respectively. Then M. Kojman and S. Shelah (Proc. AMS 131(2003), no. 5) proved that there exists a van der Waerden space which is not a Hindman space. The question whether there exists a Hindman space which is not a van der Waerden space is still open. In my talk I will show how this question about topological spaces can be reduced to a question only about Katetov order of two ideals of subsets of \(\mathbb{N}\). This result is from our joint paper with K. Kowitz, A. Kwela nad J. Tryba (Proc. AMS 150(2022), no. 2).
Location: room 605, Mathematical Institute, University of Wroclaw
Speaker: Rafał Filipów (University of Gdańsk)
Title: Does there exist a Hindman space which is not a van der Waerden space?
Abstract: Both Hindman spaces and van der Waerden spaces were defined by M. Kojman (Proc. AMS 130(2002), no. 3 and no. 6) with the aid of Hindman's finite sum theorem and van der Waerden's theorem on arithmetic progressions, respectively. Then M. Kojman and S. Shelah (Proc. AMS 131(2003), no. 5) proved that there exists a van der Waerden space which is not a Hindman space. The question whether there exists a Hindman space which is not a van der Waerden space is still open. In my talk I will show how this question about topological spaces can be reduced to a question only about Katetov order of two ideals of subsets of \(\mathbb{N}\). This result is from our joint paper with K. Kowitz, A. Kwela nad J. Tryba (Proc. AMS 150(2022), no. 2).