Hamburg Workshop on Set Theory 2015
Generalized Baire Space
20 & 21 September 2015
Hamburg (Germany)

The Hamburg Set Theory Workshop 2015 aims to provide the platform for exchange for the researchers active in the field of the set theory of the generalized Baire space. It is a satellite workshop taking place right before the beginning of the DMV 2015 in Hamburg and it is partially funded by the Deutsche Forschungsgemeinschaft (grant number LO834/12-1). The two days of the workshop will consist of two tutorials, several contributed talks and a concluding discussion session.

Everyone is cordially invited to attend.

Organizers: Giorgio Laguzzi, Wolfgang Wohofsky

Location: 20146 Hamburg, Germany. University Main Building in Siemers-Allee 1. How to get there --> From Dammtor. (~5 min walk) ;

The seminar talks will take place in the Lectures Hall J, "Magdalene Schoch Hoersaal". (How to reach it.)

Tutorials

Participants

Abstracts

Andrew Brooke-Taylor (Bristol)
On large cardinal preservation for generalized Baire space - I will discuss some observations regarding the use of large cardinal preservation arguments in the study of generalized Baire space.

Vadim Kulikov (Vienna)
The language M^kappa^+_kappa and Borel sets - The study of generalized Baire spaces is largely motivated by the connections with the theory of uncountable models. In this tutorial we will look at this from the point of view of infinitely deep languages. I will try to focus on the history and motivations behind Borel* sets and the M_{\kappa^+\kappa} language. I will finish by presenting our results with Tapani Hyttinen from 2012 on the relationship between these concepts and putting forward speculations for further research.

Giorgio Laguzzi (Freiburg)
Amoeba for uncountables - Amoeba forcings play a central role in the study of regularity properties and cardinal invariants. In particular they are important for increasing the additivity number of a given ideal. In this talk I will analyze some amoebas for different versions of Sacks forcing in 2^\kappa.

Philipp Luecke (Bonn).
Lightface Delta^1_1 subsets of omega_1^omega_1 - We say that a set of functions from omega_1 to omega_1 is Delta^1_1 if it is definable over H(omega_2) by a Delta_1-formula with parameters. It is well-known that many basic questions about the structural properties of this class are not decided by the axioms of ZFC together with large cardinal axioms. In my talk, I want to present examples of such questions that are settled by large cardinal axioms when we restrict ourselves to sets of functions defined by Delta_1-formulas whose parameters are contained in L(R).

Luca Motto Ros (Turin).
On some classification problems concerning uncountable structures and non-separable metric spaces - In mathematics one frequently deals with the problem of classifying various objects up to some natural notion of equivalence by means of (complete) invariants. In the last three decades, the notion of Borel reducibility in classical descriptive set theory has proven to be an invaluable tool in studying the complexity of many such problems. However, an intrinsic limitation to this method is that it allows us to deal just with classification problems concerning countable (algebraic) structures or separable spaces, such as separable complete metric spaces, separable Banach spaces, and so on. In this talk I will survey some recent results which demonstrate how the so-called generalized descriptive set theory can be used to overcome this limitation and treat analogous classification problems concerning uncountable structures and non-separable spaces, often leading to interesting results that significantly differ from their countable/separable counterparts. Indeed these applications of generalized descriptive set theory may be collectively viewed as a strong motivation for pursuing the study of this subject and of its surprising connections with combinatorial set theory and model theory.