# Winter School 2010

## Jörg Brendle, Alan Dow, Sy David Friedman, Menachem Magidor

## Program

This year of the tutorial lectures (each tutorial comprising of several 50 minute lectures) were devoted to advanced topics of Set Theory and were delivered by leading experts in the respective fields. Professor Menachem Magidor (Hebrew University, Jerusalem) prepared an introduction to the newest developements of PCF theory and its applications in five lectures Professor Alan Dow (University of North Carolina at Charlotte) had three lectures about the continuous images of ω*, the Čech-Stone compactification of the natural numbers and about related combinatorial problems. Professor Jörg Brendle (Kobe University, Japan) had a five part tutorial on advanced forcing techniques with an emphasis on different aspects of the iteration theory illustrated by new and old examples. Professor Sy David Friedman (Kurt Gödel Research Center, Vienna) concentrated on forcings preserving large cardinals in three lectures. The research presentations were given mainly by younger participants who presented their newest results. The topics included General Topology, Set Theory, Boolean Algebras and Forcing, Measure Theory, Descriptive Set Theory, Functional spaces and the Theory of Ultrafilters. Each day participants had time to discuss their work with colleagues. The topics of the discussions were diverse and included recent developments in set theory (research into P-ideals, generalization of cardinal characteristics of the continuum to larger cardinals, recent trends in set theoretic topology, automorphisms of ω* etc.)## Participants

Christian Adler, Boris Šobot, Jaroslav Šupina, Bohuslav Balcar, Paweł Barbarski, Aleksander Błaszczyk, Wojciech Bielas, Piotr Borodulin-Nadzieja, Jörg Brendle, Andrew Brooke-Taylor, Lev Bukovský, David Chodounský, Alan Dow, Andreas Fackler, Barnabas Farkas, Jana Flašková, Marta Frankowska, Sy David Friedman, Petr Glivický, Michał Gołębiowski, Rafal Gruszczynski, Magdalena Grzech, Radek Honzík, Michael Hrušák, Istvan Juhasz, Piotr Kalemba, Kaisa Kangas, Teppo Kankaanpää, Yurii Khomskii, Adam Kolipiński, Zdzisław Kosztołowicz, Peter Krautzberger, Wieslaw Kubiś, Andrzej Kucharski, Menachem Magidor, Hiroaki Minami, Miguel Angel Mota, Nikodem Mrożek, Andrzej Nowik, Aleksandar Pavlović, Tomáš Pazák, Francesco Piccoli, Szymon Plewik, Alexander Primavesi, Robert Ralowski, Růžena Roháčková, Dan Rosendorf, Marcin Sabok, Robin Scholz, Petr Simon, Lájos Soukup, Daniel Soukup, Michal Staš, Victor Torres Perez, Slawomir Turek, Toshimichi Usuba, Benjamin Vejnar, Jonathan Verner, Mate Vizer, Martin Weese, Thilo Weinert, Anna Wojciechowska, Lyubomyr Zdomskyy, Szymon Zeberski,## Photos

- Photos by A. Pavlović
- The 2010 Wednesday Trip (by J. Flašková)
- Photos by P. Simon

## Talks, slides, abstracts

Speaker | Title | Abstract/Slides |
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