Winter School 2010

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


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.)


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,


Talks, slides, abstracts

Jaroslav ŠupinawQN spaces slides
Aleksander BłaszczykTransversal and independent topologies slides
Piotr Borodulin-NadziejaMeasure recognition problems slides
Jörg BrendleAspects of iterated forcing (I., II., III., IV.) slides
Andrew Brooke-TaylorIndestructibility of Vopěnka Cardinal slides
David ChodounskýRapid Filters and Guided Gregorieff Forcing slides
Alan DowMoron maps and subspaces of N* slides
Alan DowMoron maps and subspaces of N* (under PFA) slides
Alan DowMoron maps and subspaces of N* (extending PFA) slides
Jana FlaškováRemarks on Q-points and Rapid Ultrafilters slides
Sy David FriedmanForcings which Preserve Large Cardinals slides
Rafal GruszczynskiShort introduction to mereology slides
Radek HonzíkLifting arguments slides
Istvan JuhaszConvergence and character spectra of compacta slides / paper
Zdzisław KosztołowiczCharacterizing Chainable and Tree-like Continua slides
Peter KrautzbergerSome new results on union ultrafilters slides
Wieslaw KubiśRetractive Linear Orderings slides
Andrzej KucharskiOpen-Open Game of Uncountable Length slides
Menachem MagidorCardinal Arithmetic / paper
Andrzej NowikMeasurable Hamel functions slides
Aleksandar PavlovićA "mean" sequence in Boolean algebras slides
Szymon PlewikOn skeletal maps slides
Alexander PrimavesiExtending the Classical Results on Club Guessing slides
Robert RalowskiLuzinnes on the Real Line slides
Marcin SabokForcing, ideals and degrees of reals slides
Daniel SoukupCross-like constructions and refinementsabstract slides
Lájos SoukupThe Joy of Elementary Submodels slides
Michal StašRegular properties on the real line slides
Victor Torres PerezWeak Reflection Principle, Saturation of NS and Diamonds slides
Szymon ZeberskiInscribing Baire-nonmeasurable sets slides
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