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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A.R.D. Mathias Alan Dow Alekos Kechris Aleksander Cieślak Aleksandra Kwiatkowska Alexei Kolesnikov Andreas Blass Andrés Caicedo Andrés Villaveces Andrew BrookeTaylor Andrew Marks Andrew Toms Andy Zucker Antonio Avilés Anush Tserunyan Ari Brodsky Arthur Apter Asaf Karagila Asger Tornquist Ashutosh Kumar Assaf Hasson Assaf Rinot Barnabas Farkas Benjamin Miller Bill Chen Bill Mitchell Boban Velickovic Boris Zilber Brent Cody Burak Kaya Carlos Di Prisco Carlos MartinezRanero Chris LambieHanson Christina Brech Clinton Conley Daisuke Ikegami Damian Sobota Dana Bartošová Daniel Rodriguez Daniel Soukup David Aspero David Chodounsky David Fernández Bretón David J. Fernández Bretón David Marker David Milovich Diana Ojeda Diego Alejandro Mejia Dikran Dikranjan Dilip Raghavan Dima Sinapova Dimitrios Vlitas Egbert Thümmel Erez Shochat Erin Carmody Farmer Schlutzenberg Frank Stephan Franklin Tall Gregory Cherlin Grigor Sargsyan Grzegorz Plebanek Gunter Fuchs Heike Mildenberger Hiroshi Sakai Hugh Woodin Ilijas Farah Ioannis Souldatos Isaac Goldbring István Juhász Itay Neeman James Cummings Jan Grebík Jan Stary Jan van Mill Janusz Pawlikowski Jay Williams Jean Larson Jindra Zapletal Joan Bagaria Joel David Hamkins John Baldwin John Clemens John Krueger John Steel Jonathan Verner Jordi LopezAbad Jörg Brendle Jose Iovino Jouko Väänänen Julien Melleray Juliette Kennedy Juris Steprans Justin Moore K. P. Hart Kaethe Minden Katharina Dupont Konstantinos Tyros Lajos Soukup Laura Fontanella Liljana Babinkostova Lionel Nguyen Van The Liuzhen Wu Luca Motto Ros Luz María García Ávila Lynn Scow Lyubomyr Zdomskyy Marcin Michalski Marcin Sabok Marion Scheepers Martin Goldstern Martin Zeman Martino Lupini Maryanthe Malliaris Masaru Kada Mati Rubin Matteo Viale Matthew D. Foreman Melvin Fitting Menachem Kojman Menachem Magidor Merlin Carl Michael Hrusak Michal Doucha Miguel Angel Mota Miha Habic Mike Pawliuk Mikhail Tkachenko Miodrag Sokic Mirna Džamonja Miyamoto Tadatoshi Monroe Eskew Moti Gitik Nadav Meir Nam Trang Natasha Dobrinen Norman Perlmutter Omer Ben Neria Osvaldo Guzman Osvaldo Guzmán González Paul Larson Paul McKenney Peng Yinhe Peter Holy Peter Koellner Peter Koepke Peter Komjath Peter Krautzberger Petr Simon Philip Welch Philipp Lücke Philipp Schlicht Pierre Simon Piotr BorodulinNadzieja Piotr Koszmider Ralf Schindler Randall Holmes Robert Ralowski Robin TuckerDrob Rodrigo R. Dias Roman Kossak Saharon Shelah Sakaé Fuchino Salma Kuhlmann Samuel Coskey Scott Cramer Scott Schneider Sean Cox Sebastien Vasey Sergei Artemov Shehzad Ahmed Simon Thomas Slawomir Solecki Spencer Unger Stefan Geschke Stevo Todorcevic Su Gao Sy David Friedman Szymon Zeberski Teruyuki Yorioka Thilo Weinert Thomas Johnstone Timothy Trujillo Todd Eisworth Todor Tsankov Tomek Bartoszynski Toshimichi Usuba Trevor Wilson Tristan Bice Uri Abraham Vera Fischer Victor Torres Perez Victoria Gitman Vincenzo Dimonte Wieslaw Kubis Will Boney Wojciech Stadnicki Wolfgang Wohofsky Yair Hayut Yizheng Zhu Yurii KhomskiiCategories
Recent discussions
 10th Young Set Theory Workshop, Edinburgh, July 1014, 2017  Set Theory Talks on 6th Young Set Theory Workshop, June 1014, 2013
 10th Young Set Theory Workshop, Edinburgh, July 1014, 2017  Set Theory Talks on 9th Young Set Theory Workshop, Copenhagen, June 1317, 2016
 10th Young Set Theory Workshop, Edinburgh, July 1014, 2017  Set Theory Talks on 8th Young Set Theory Workshop, Jerusalem, October 2530, 2015
 1st Irvine Conference on Descriptive Inner Model Theory and HOD Mice, July 1829 2016  Set Theory Talks on Inner Model Theory events in California, June, 2014
 saf on Assaf Rinot: The strength of the generalized Souslin hypothesis
 10th Young Set Theory Workshop, Edinburgh, July 1014, 2017  Set Theory Talks on 6th Young Set Theory Workshop, June 1014, 2013
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