KNAW Academy Colloquium

Generalised Baire Spaces

Amsterdam, The Netherlands

Master Class: 22 August 2018 / Colloquium: 23–24 August 2018


Organisers. Lorenzo Galeotti, Benedikt Löwe, Philipp Lücke.

Descriptive set theory and set theory of the reals traditional deal with well-known and well-studied topological spaces such as the real numbers, Cantor space, and Baire space. In recent years, set theorists are increasingly interested in the uncountable analogues 2κ of the Cantor space (generalised Cantor space) and κκ of the Baire space (generalised Baire space) for uncountable cardinals κ.

While many concepts from the classical setting can be transferred to generalised Baire space and some classical results remain true at uncountable cardinals, in general the rich combinatorial nature of uncountable cardinals causes the theory of the corresponding spaces to differ significantly e.g., notions which are equivalent in the classical setting can lead to different notions in the generalised theory. Phenomena like this shed light on structures and properties otherwise hidden in the classical setting.

The study of generalised Baire spaces has developed into a research area in its own right with a rich overarching theory, internally motivated open questions (cf. Khomskii, Laguzzi, Löwe, Sharankou 2016) and an active research community, combining methods and techniques from several branches of set theory like uncountable combinatorics, forcing, large cardinals, inner models and classical descriptive set theory and also involves techniques from classical model theory. The community met first at the Amsterdam Set Theory Workshop 2014 in November 2014, then at a satellite workshop to the German mathematics congress in Hamburg in September 2015, and finally at a workshop at the Hausdorff Center for Mathematics in Bonn in September 2016. This Academy Colloquium is a reunion of the community after a hiatus of two years.

The Colloquium will be preceded by an associated KNAW Master Class for postgraduate students in order to prepare them for the talks at the Colloquium. The KNAW Master Class will take place on 22 August 2018.

Wednesday, 22 August 2018: Master Class

9:00-10:15 Registration
10:15-11:00 Andreas Blass
(Ann Arbor MI, U.S.A.)
The classical theory of cardinal invariants, Part 1
11:00-11:15 Coffee Break
11:15-12:00 Jouko Väänänen
(Helsinki, Finland)
Generalized Baire spaces - basic concepts and motivation, Part 1
12:00-12:15 Coffee Break
12:15-13:00 Andrew Brooke-Taylor
(Leeds, England)
Generalising the weak compactness of ω, Part 1
13:00-14:00 Lunch break
14:00-14:45 Philipp Schlicht
(Bonn, Germany)
Descriptive set theory in the setting of generalized Baire spaces, Part 1
14:45-15:00 Coffee Break
15:00-15:45 Andreas Blass
(Ann Arbor MI, U.S.A.)
The classical theory of cardinal invariants, Part 2
15:45-16:00 Coffee Break
16:00-16:45 Jouko Väänänen
(Helsinki, Finland)
Generalized Baire spaces - basic concepts and motivation, Part 2
16:45-17:00 Coffee Break
17:00-17:45 Andrew Brooke-Taylor
(Leeds, England)
Generalising the weak compactness of ω, Part 2
17:45-18:00 Coffee Break
18:00-18:45 Philipp Schlicht
(Bonn, Germany)
Descriptive set theory in the setting of generalized Baire spaces, Part 2
 
 

Thursday, 23 August 2018: Colloquium

Friday, 24 August 2018: Colloquium

10:30-10:45 Opening Dima Sinapova
(Chicago IL, U.S.A.)
Kurepa trees and spectra of Lω1-sentences
10:45-11:00 Luca Motto Ros
(Torino, Italy)
Generalized descriptive set theory under I0
11:00-11:15
11:15-11:30 Coffee Break
11:30-11:45 Coffee Break Dorottya Sziraki
(Budapest, Hungary)
Open colorings, perfect sets and games on generalized Baire spaces
11:45-12:00 Daisuke Ikegami
(Tokyo, Japan)
On preserving AD by forcing
12:00-12:15 Vera Fischer
(Vienna, Austria)
More ZFC inequalities between cardinal invariants Marlene Koelbing
(Vienna, Austria)
Aronszajn and Kurepa trees
12:15-12:30 Natasha Dobrinen
(Denver CO, U.S.A.)
Perfect tree forcings for singular carinals
12:30-12:45 Sarka Stejskalova
(Vienna, Austria)
The tree property
12:45-13:00 Lunch Break Lunch Break
13:00-13:15
13:15-13:30
13:30-13:45
13:45-14:00
14:00-14:15 Radek Honzik
(Prague, Czech Republic)
Compactness principles and cardinal invariants Diana Carolina Montoya
(Vienna, Austria)
Some inequalities between generalized cardinal invariants
14:15-14:30
14:30-14:45
14:45-15:00 Coffee Break Coffee Break
15:00-15:15 Thomas Baumhauer
(Vienna, Austria)
Shelah's generalised null ideal

Sandra Müller
(Vienna, Austria)
and
David Schrittesser
(Vienna, Austria)
Lebesgue's Density Theorem for Tree Forcing Ideals
15:15-15:30 Filippo Calderoni
(Torino, Italy)
Completeness and universality for analytic equivalence relations
15:30-15:45 Vincenzo Dimonte
(Udine, Italy)
Silver dichotomy for countable cofinalities

Peter Holy
(Bonn, Germany)
and
Wolfgang Wohofsky
(Kiel, Germany)
The Edinburgh topology
15:45-16:00 Tapani Hyttinen
(Helsinki, Finland)
Classification theory in generalized Baire spaces
16:00-16:15 Liuzhen Wu
(Beijing, China)
(*), MM and Π1 definability of NSω1
16:15-16:30 Coffee Break
16:30-16:45 Coffee Break
16:45-17:00 David Asperó
(Norwich, England)
Special ℵ2-Aronszajn trees and GCH
17:00-17:15 Yurii Khomskii
(Hamburg, Germany)
Laver Trees in the Generalised Baire Space
17:15-17:30
17:30-17:45 Closing Discussion
17:45-18:00 Giorgio Laguzzi
(Freiburg, Germany)
κ-trees and Cohen κ-sequences
18:00-18:15
18:15-18:30
18:30-18:45
18:45-19:00
19:00– Conference Dinner
Last changed: 13 March 2018