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,
Talks, slides, abstracts
| Speaker | Title | Download |
| Radek Honzík | Lifting arguments | slides
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| Rafal Gruszczynski | Short introduction to mereology | slides
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| Jana Flašková | Remarks on Q-points and Rapid Ultrafilters | slides
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| Jaroslav Šupina | wQN spaces | slides
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| Michal Staš | Regular properties on the real line | slides
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| Istvan Juhasz | Convergence and character spectra of compacta | paper slides
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| Peter Krautzberger | Some new results on union ultrafilters | slides
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| Piotr Borodulin-Nadzieja | Measure recognition problems | slides
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| Aleksandar Pavlović | A "mean" sequence in Boolean algebras | slides
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| Aleksander Błaszczyk | Transversal and independent topologies | slides
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| Wieslaw Kubiś | Retractive Linear Orderings | slides
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| Andrzej Kucharski | Open-Open Game of Uncountable Length | slides
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| Robert Ralowski | Luzinnes on the Real Line | slides
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| Szymon Zeberski | Inscribing Baire-nonmeasurable sets | slides
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| Daniel Soukup | Cross-like constructions and refinements | abstract slides
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| Andrzej Nowik | Measurable Hamel functions | slides
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| Zdzisław Kosztołowicz | Characterizing Chainable and Tree-like Continua | slides
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| Marcin Sabok | Forcing, ideals and degrees of reals | slides
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| Victor Torres Perez | Weak Reflection Principle, Saturation of NS and
Diamonds | slides
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| Sy David Friedman | Forcings which Preserve Large Cardinals | slides
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| David Chodounský | Rapid Filters and Guided Gregorieff Forcing | slides
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| Alan Dow | Moron maps and subspaces of N* | slides
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| Alan Dow | Moron maps and subspaces of N* (under PFA) | slides
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| Alan Dow | Moron maps and subspaces of N* (extending PFA) | slides
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| Menachem Magidor | Cardinal Arithmetic | paper
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| Szymon Plewik | On skeletal maps | slides
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| Jörg Brendle | Aspects of iterated forcing (I., II., III., IV.) | slides
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| Andrew Brooke-Taylor | Indestructibility of Vopěnka Cardinal | slides
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| Alexander Primavesi | Extending the Classical Results on Club Guessing | slides
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| Lyubomyr Zdomskyy | Combinatorial Properties of Open Covers of Products with Scales |
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| Lájos Soukup | The Joy of Elementary Submodels | slides
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