Abstract: Strongly summable ultrafilters are a variety of ultrafilters that relate with Hindman’s finite sums theorem in a way that is somewhat analogous to that in which Ramsey ultrafilters relate to Ramsey’s theorem. It is known that the existence of these ultrafilters cannot be proved in ZFC, however such an existencial statement follows from having the covering of meagre to equal the continuum. Furthermore, using ultraLaver forcing in a short finite support iteration, it is possible to get models with strongly summable ultrafilters and a small covering of meagre, and these models will also have small dominating number. Using this ultraLaver forcing in a countable support iteration to get a model with small covering meagre and strongly summable ultrafilters is considerably harder, but it can be done and in this talk I will explain how (it involves a characterisation of a certain kind of strongly summable ultrafilter in terms of games). Interesingly, this way we also get the dominating number equal to the continuum, unlike the previously described model.
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 February 12: 2nd Arctic Set Theory Workshop, February 1217, 2015
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A.R.D. Mathias Alan Dow Alekos Kechris Aleksandra Kwiatkowska Alex Rennet Alexei Kolesnikov Alf Dolich Andreas Blass Andrés Caicedo Andrew BrookeTaylor Andrew Marks Andrew Toms Andy Zucker Antonio Avilés Antonis Achilleos Anush Tserunyan Ari Brodsky Arthur Apter Asaf Karagila Asger Tornquist Ashutosh Kumar Assaf Hasson Assaf Rinot Barnabas Farkas Benjamin Miller Bill Mitchell Boban Velickovic Burak Kaya Carlos Di Prisco Carlos MartinezRanero Chris LambieHanson Christina Brech Claude Laflamme Clinton Conley Daisuke Ikegami Dana Bartošová Daniel Soukup David Aspero David Chodounsky David J. Fernández Bretón David Kerr David Marker David Milovich Diana Ojeda Diego Alejandro Mejia Dikran Dikranjan Dilip Raghavan Dima Sinapova Dimitrios Vlitas Egbert Thümmel Erez Shochat Farmer Schlutzenberg François Dorais Frank Stephan Franklin Tall Giorgio Laguzzi Graham Priest Gregory Cherlin Grigor Sargsyan Grzegorz Plebanek Gunter Fuchs Harvey Friedman Heike Mildenberger Hiroshi Sakai Hugh Woodin Ilijas Farah Isaac Goldbring István Juhász Itay Neeman James Cummings Jan Grebík Jan van Mill Jana Flašková Janusz Pawlikowski Jay Williams Jean Larson Jerry Vaughan Jindra Zapletal Joan Bagaria Joel David Hamkins Johan van Benthem John Baldwin John Krueger John Steel Jordi LopezAbad Jörg Brendle Jose Iovino Jose Mijares Jouko Väänänen Juliette Kennedy Juris Steprans Justin Moore K. P. Hart Kaethe Minden Katharina Dupont Konstantinos Tyros Lajos Soukup Laura Fontanella Liuzhen Wu Luca Motto Ros Luz María García Ávila Lynn Scow Lyubomyr Zdomskyy Manuel Alves Marcin Michalski Marcin Sabok Marion Scheepers Martin Goldstern Martin Zeman Martino Lupini Maryanthe Malliaris Masaru Kada Matteo Viale Matthew D. Foreman Melvin Fitting Menachem Kojman Menachem Magidor Merlin Carl Michael Hrusak Michal Doucha Miguel Angel Mota Mikhail Tkachenko Miodrag Sokic Mirna Džamonja Miyamoto Tadatoshi Monroe Eskew Moti Gitik Nadav Meir Nam Trang Natasha Dobrinen Norman Perlmutter Omar Selim Omer Ben Neria Osvaldo Guzmán González Paul Larson Paul McKenney Peter Holy Peter Koellner Peter Koepke Peter Komjath Peter Krautzberger Petr Simon Philip Welch Philipp Lücke Philipp Schlicht Pierre Simon Piotr BorodulinNadzieja Piotr Koszmider Qi Feng Ralf Schindler Randall Holmes Robert Ralowski Robin TuckerDrob Rodrigo R. Dias Roman Kossak Russell Miller Saharon Shelah Sakaé Fuchino Samuel Coskey Scott Cramer Scott Schneider Sean Cox Sebastien Vasey Sergei Artemov Shehzad Ahmed Simon Thomas Slawomir Solecki Spencer Breiner Spencer Unger Stefan Geschke Stevo Todorcevic Su Gao Sy David Friedman Ted Slaman Teruyuki Yorioka Thilo Weinert Thomas Johnstone Timothy Trujillo Todd Eisworth Todor Tsankov Tomek Bartoszynski Toshimichi Usuba Trevor Wilson Tristan Bice Ulises Ariet Ramos Garcia Uri Abraham Vera Fischer Victor Torres Perez Victoria Gitman Vincenzo Dimonte Whanki Lee Wieslaw Kubis Will Boney Wojciech Stadnicki Wolfgang Wohofsky Yang Yue Yasuo Yoshinobu Yizeng Zhu Yurii Khomskii Zoe ChatzidakisCategories
Recent discussions
 Neugebauer’s theorem  A kind of library on Andrés Caicedo: Coanalytic uniformization
 David on Winter School, Jan 31 – Feb 7, 2015
 8th Young Set Theory Workshop, October 2530, 2015  Set Theory Talks on 6th Young Set Theory Workshop, June 1014, 2013
 saf on MidAtlantic Mathematical Logic Seminar, October 2526, 2014
 David on MidAtlantic Mathematical Logic Seminar, October 2526, 2014
 Neugebauer’s theorem  A kind of library on Andrés Caicedo: Coanalytic uniformization
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