Intranet

Infinite Combinatorics

prof. dr hab. Ryszard Frankiewicz (IM PAN), prof. dr hab. Bogdan Węglorz (UKSW), dr Joanna Jureczko (PWr)

Currently, we are focusing on the following topics:

  1. The Enflo-Rosenthal problem (1973),

  2. Gowers' dichotomy theorem (1993),

  3. The Drewnowski-Roberts problem (1991) concerning certain properties of the space l∞/c0,

  4. Partitioners (Baumgartner-Wesse (1982)).

Upcoming meetings will be held on May 9, 16, 23, and 29 (instead of May 30), June 6, and June 13.

In the spring semester of 2018/2019, we will continue our discussions around the following topics:

  1. The Enflo-Rosenthal problem (1973),

  2. The Kuratowski problem (1935),

  3. Gitik-Shelah theorem (1989),

  4. Gowers' dichotomy theorem (1993),

  5. The Drewnowski-Roberts problem (1991) concerning certain properties of the space l∞/c0.

Upcoming meetings will be held on March 7, 14, 21, 28, April 4, and 11, 2019. The seminar will resume after May 5, 2019.

 

From February 2019, we will continue our discussions on the Enflo-Rosenthal problem (1973), and in addition, we will focus on:

  1. Exploring the connections between the existence of Kuratowski partitions (Kuratowski problem from 1935) and the Gitik-Shelah theorem (1989),

  2. Considerations around Gowers' dichotomy theorem (1993),

  3. The Drewnowski-Roberts problem (1991) concerning certain properties of the space l∞/c0.

Upcoming meetings will be held on February 1 (Friday), February 5 (Tuesday), February 8 (Friday), February 13 (Wednesday), and February 28 (Thursday).

From January 2019, we will continue our discussions on the Enflo-Rosenthal problem (1973), and in addition, we will focus on:

  1. Exploring the connections between the existence of Kuratowski partitions (Kuratowski problem from 1935) and the Gitik-Shelah theorem (1989),

  2. Considerations around Gowers' dichotomy theorem (1993),

  3. The Drewnowski-Roberts problem (1991) concerning certain properties of the space l∞/c0.

Upcoming meetings will be held on January 10, 2019, January 17, January 24, and January 30 (Wednesday instead of January 31).

The seminar will resume in the spring semester of 2018/2019 according to the academic calendar of the Wrocław University of Science and Technology (http://pwr.edu.pl/kalendarz-akademicki-semestr-zimowy-2018-2019).

In the winter semester of 2018/2019*, the seminar will be dedicated to two problems:

1. The Enflo-Rosenthal problem (1973): Let Lp(μ) be non-separable. Can Lp(μ) be a subspace of a Banach space with an unconditional basis?

2. Investigating the structure of the algebra P(ω)/ ᴧ, where ᴧ denotes the family of subsets of ω with asymptotic density 0.

Upcoming meetings will be held on October 18, October 25, November 8, November 15, November 23 (Friday instead of November 22), November 29, December 6, December 12 (Wednesday instead of December 13), December 20, January 10, 2019, January 17, January 24, and January 30 (Wednesday instead of January 31).

After the inter-semester break*, the seminar will resume.

*according to the academic calendar of the Wrocław University of Science and Technology (http://pwr.edu.pl/kalendarz-akademicki-semestr-zimowy-2018-2019).

2017-12-05 at 15:15 in room C4-245 (Wrocław University of Science and Technology)

Sławomir Szczepaniak (Wrocław University of Science and Technology)

"Transfinite bases in Banach spaces - continuation"

Abstract:

We discuss some analytical and set-theoretic aspects of the existence of long basic sequences in non-separable Banach spaces.

2017-11-28 at 15:15 in room C4-245 (Wrocław University of Science and Technology)

Sławomir Szczepaniak (Wrocław University of Science and Technology)

"Transfinite bases in Banach spaces - continuation"

Abstract:

We discuss some analytical and set-theoretic aspects of the existence of long basic sequences in non-separable Banach spaces.

2017-11-21 at 15:15 in room C4-245 (Wrocław University of Science and Technology)

Sławomir Szczepaniak (Wrocław University of Science and Technology)

"Transfinite bases in Banach spaces"

Abstract:

We discuss some analytical and set-theoretic aspects of the existence of long basic sequences in non-separable Banach spaces.

2017-11-14, at 15:15 in room C4-245 (Wrocław University of Science and Technology)

Sławomir Szczepaniak (Wrocław University of Science and Technology)

"Dugundji Theorem for metrizable and non-metrizable spaces - continuation"

Abstract:

We discuss some variations of the Dugundji Theorem.

2017-11-07, at 15:15 in room C4-245 (Wrocław University of Science and Technology)

Sławomir Szczepaniak (Wrocław University of Science and Technology)

"Dugundji Theorem for metrizable and non-metrizable spaces"

Abstract:

We discuss some variations of the Dugundji Theorem.

2017-04-25, at 17:30 in room 403

Bogdan Węglorz (Cardinal Stefan Wyszyński University in Warsaw)

"Some aspects of forcing - continuation"

Abstract:

There will be presented some aspects of forcing.

2017-03-28, at 17:30 in room 403

Bogdan Węglorz (Cardinal Stefan Wyszyński University in Warsaw)

"Some aspects of forcing"

Abstract:

There will be presented some aspects of forcing.

2017-03-21, at 17:30 in room 403

Bogdan Węglorz (Cardinal Stefan Wyszyński University in Warsaw)

"Models of Set Theory"

Abstract:

There will be presented examples of models of set theory.

2017-03-14, at 17:00 in room 403

Tomasz Weiss (Cardinal Stefan Wyszyński University in Warsaw)

"The proof of add(M ∩ N, N) = add(M)"

Abstract:

We prove that add(M ∩ N, N) = add(M) using ZFC only.

2017-02-28, at 18:30 in room 403

Tomasz Weiss (Cardinal Stefan Wyszyński University in Warsaw)

"On the additivity and cofinality of the intersection ideal M ∩ N" - continuation

Abstract:

We prove that the additivity of the intersection ideal M ∩ N is equal to the additivity of the ideal N of null sets in the Cantor space 2w. We show that a similar result holds also for the cofinality number of the above ideals.

2017-02-21, at 18:30 in room 403

Tomasz Weiss (Cardinal Stefan Wyszyński University in Warsaw)

"On the additivity and cofinality of the intersection ideal M ∩ N" - continuation

Abstract:

We prove that the additivity of the intersection ideal M ∩ N is equal to the additivity of the ideal N of null sets in the Cantor space 2w. We show that a similar result holds also for the cofinality number of the above ideals.

2017-01-24, at 18:30 in room 403

Tomasz Weiss (Cardinal Stefan Wyszyński University in Warsaw)

"On the additivity and cofinality of the intersection ideal M ∩ N" - continuation

Abstract:

We prove that the additivity of the intersection ideal M ∩ N is equal to the additivity of the ideal N of null sets in the Cantor space 2w. We show that a similar result holds also for the cofinality number of the above ideals.

2017-01-11, at 9:30 in room 106

Tomasz Weiss (Cardinal Stefan Wyszyński University in Warsaw)

"On the additivity and cofinality of the intersection ideal M ∩ N"

Abstract:

We prove that the additivity of the intersection ideal M ∩ N is equal to the additivity of the ideal N of null sets in the Cantor space 2w. We show that a similar result holds also for the cofinality number of the above ideals.

2016-12-14, at 9:30 in room 106

Joanna Jureczko (Cardinal Stefan Wyszyński University in Warsaw)

"On Kuratowski partitions" - continuation

Abstract:

It will be presented problems concerning the existence of Kuratowski partitions.

2016-12-07, at 9:30 in room 106

Joanna Jureczko (Cardinal Stefan Wyszyński University in Warsaw)

"On Kuratowski partitions"

Abstract:

It will be presented problems concerning the existence of Kuratowski partitions.

2016-11-30, at 9:30 in room 106

Ryszard Frankiewicz (Institute of Mathematics of Polish Academy of Sciences)

"On asymptotic density"

Abstract:

It will be presented some problems concerning asymptotic density.

2016-11-23, at 9:30 in room 106

Joanna Jureczko (Cardinal Stefan Wyszyński University in Warsaw)

"Kuratowski partitions on the structure of Ellentuck topology" - continuation

Abstract:

It will be presented the existence of Kuratowski partitions in some structures, especially Ellentuck topology.

2016-11-16, at 9:30 in room 106

Joanna Jureczko (Cardinal Stefan Wyszyński University in Warsaw)

"Kuratowski partitions on the structure of Ellentuck topology" - continuation

Abstract:

It will be presented the existence of Kuratowski partitions in some structures, especially Ellentuck topology.

2016-11-09, at 9:30 in room 106

Joanna Jureczko (Cardinal Stefan Wyszyński University in Warsaw)

"Kuratowski partitions on the structure of Ellentuck topology"

Abstract:

It will be presented the existence of Kuratowski partitions in some structures, especially Ellentuck topology.