# Winter School 2009 (Forcing for the faint of heart)

## U. Abraham, P. Koszmider, J. Pawlikowski, L. Soukup

## Program

The lectures in the tutorial track focused on the basics of forcing theory and its applications. The lectures covered elementary as well as intermediate topics. U. Abraham had a tutorial on forcing with side conditions and the P-ideal dichotomy. P. Koszmider focused on iterated forcing and showed how to force MA, non CH and no Kurepa tree. J. Pawlikowski gave lectures on reals and forcing and L. Soukup focused on forcing and combinatorics. The research track contained the usual mix of research presentations from general topology, set theory, measure theory and related fields.## Participants

Uri Abraham, Christian Adler, Antonio Aviles, Boris Šobot, Jaroslav Šupina, Bohuslav Balcar, Taras Banakh, Dana Bartošová, Aleksander Błaszczyk, Wojciech Bielas, Piotr Borodulin-Nadzieja, David Chodounsky, Michal Doucha, Peter Elias, Jana Flašková, Sy David Friedman, Jakub Gismatullin, Magdalena Grzech, Edward Grzegorek, Radek Honzík, Michael Hrušák, Piotr Kalemba, Pawel Kawa, Archil Kipiani, Adam Kolipiński, Piotr Koszmider, Peter Krautzberger, Mikołaj Krupski, Wieslaw Kubis, Andrzej Kucharski, Marcin Kysiak, Michal Machura, Henryk Michalewski, Nikodem Mrożek, Andrzej Nowik, Aleksandar Pavlovic, Janusz Pawlikowski, Tomáš Pazák, Marcin Petrykowski, Szymon Plewik, Robert Rałowski, Ulises Ariet Ramos García, Marcin Sabok, Alicja Samulewicz, Robin Scholz, Omar Selim, Petr Simon, Daniel Soukup, Lájos Soukup, Michal Staš, Wojciech Stadnicki, Jan Starý, Andrzej Starosolski, Marcin Szyszkowski, Osvaldo Alfonso Téllez Nieto, Egbert Thümmel, Urszula Trzópek, Kostas Tsaprounis, Luis Turcio, Jonathan Verner, Thilo Weinert, Wolfgang Wohofsky, Anna Wojciechowska, Jindřich Zapletal, Lyubomyr Zdomskyy, Szymon Zeberski, Ondřej Zindulka## Photos

- Photos by M. Kysiak
- Photos by A. Pavlović
- Photos by D. Soukup
- Photos by J. Verner
- Photos by P. Simon

If

**you**have some photos from the Winter School you would like to share with others, please send them (or a link to a gallery) to info@winterschool.eu.

## Downloads

A poster for the conference can be downloaded**here.**

**Material accompanying the talk of U. Abraham**

*U. Abraham*: Lecture notes on the P-ideal dichotomy*J. E. Baumgartner*: All ℵ_{1}-dense sets of reals can be isomorphic*S. Shelah*: Independence Results*U. Abraham, M. Rubin, S. Shelah*: On the Consistency of some Partition Theorems for Continuous Colorings, and the structure of ℵ_{1}-dense Real Order Types

**Forcing without tears (talks of L. Soukup)**

The talks of L. Soukup on forcing can be downloaded from his website here. For your convenience we have provided direct links to the talks:

**Entree to Generic Extensions and Set Theory**

(B. Balcar, T. Pazák and J. Verner)

Preliminary versions of an Entree to forcing prepared especially for this conference is available for download:

- Chapter 1: Prerequisites
- Chapter 2: Orderings and Boolean algebras
- Chapter 3: Forcing notions and Generic filters
- Chapter 4: Classical examples of Forcing notions
- Chapter 5: The Forcing Relation
- Chapter 6: Generic extensions
- Chapter 7: Solovay's model
- References

Please note that this version is far from finished and may contain many mistakes. If you come across some mistake or a place which is not clear, please let us know so that we can correct it.

## Talks, slides, abstracts

Speaker | Title | Download |

Jana Flašková | Some ultrafilters on natural numbers | slides |

Wieslaw Kubis | Finitely determined compacta | slides |

Osvaldo Alfonso Téllez Nieto | Extremally Disconnected Topological Groups | slides |

Ulises Ariet Ramos García | Countable Fréchet Groups | slides |

Marcin Sabok | Playing with forcing | slides |

Marcin Szyszkowski | Weak symmetry | slides |

Marcin Kysiak | On Bernstein sets, kappa-coverings and quotient gr | slides |

Archil Kipiani | On cardinalityes of automorphism groups of uniform | slides |

Piotr Kalemba | Hausdorff gaps reconstructed from Luzin gaps | slides |

Henryk Michalewski | Examples of complete pairs of coanalytic sets | slides |

Jindřich Zapletal | Forcing and Ramsey Theorems | slides |

Ondřej Zindulka | Every M-additive set is E-additive | slides |

Piotr Koszmider | Examples concerning generic sets | slides |

Aleksandar Pavlovic | Several Topologies on P(omega) | slides |

Boris Šobot | Games on Boolean Algebras of Uncountable Length | slides |

Sy David Friedman | Forcing when there are Large Cardinals | slides |

Piotr Koszmider | Some examples concerning forcing | slides |

Uri Abraham | P-Ideal Dichotomy I. | slides |

Peter Elias | On additivity of permitted sets | slides |

Dana Bartošová | Span and Chainability in Non-metric Continua | slides |

Uri Abraham | P-Ideal Dichotomy II. | slides |

Peter Krautzberger | Forcing Constructions of Idempotent Ultraﬁlters | slides |

Thilo Weinert | Does BAAFA decide the size of the continuum? | slides |

Radek Honzík | Global failure of SCH and Easton functions | slides |

Szymon Zeberski | Structural properties of orderings on multisets | slides |

Uri Abraham | P-Ideal Dichotomy III. | slides |

Taras Banakh | Finite chain condition and packing completeness fo | slides |

Tomáš Pazák | Classification of new reals | slides |

Piotr Koszmider | Examples concerning iterated forcing II | slides |