Seminars & Colloquia Calendar
The tree property
Dima Sinapova (Univ. of Illinois at Chicago)
Location: Hill 705
Date & time: Friday, 05 April 2019 at 4:00PM - 5:00PM
Abstract: Two central themes in logic are how much the universe of sets resembles Gödel's constructible universe \(L\) versus what is possible from forcing and large cardinals. Both are addressed by using infinite combinatorics to investigate how much compactness can be obtained in the universe. Compactness is the phenomenon when a given property holding for every smaller substructure of some object implies that property holds for the object itself. This is usually a consequence of large cardinals, and tends to fail in \(L\).
A key instance of compactness is the tree property, which states that every tree of height \(\kappa\) and levels of size less than \(\kappa\) has a cofinal branch. Informally, this principle is a generalization of König's infinity lemma to uncountable cardinals. It turns out that the tree property and certain strengthenings capture the combinatorial essence of large cardinals. An old project in set theory is to force the tree property (and some strengthenings) at every regular cardinal greater than \(\aleph_1\). I will go over the background and then discuss some recent results giving the state of the art of this project.
R. Shapiro Organizer's Page
Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page
Brooke Logan
Wujun Zhang Organizer's webpage
Ziming Shi, Sagun Chanillo, Xiaojun Huang, Chi Li, Jian Song Seminar website Old seminar website
Swastik Kopparty, Sepehr Assadi Seminar webpage
Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage
Brooke Ogrodnik, Website
Robert Dougherty-Bliss and Doron Zeilberger --> homepage
Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage
Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage
Jason Saied Seminar webpage
Brian Pinsky, Rashmika Goswami website
Quentin Dubroff Organizer's webpage
James Holland; Organizer website
Edna Jones Organizer's webpage
Brooke Ogrodnik website
Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage
Organizer: Luochen Zhao
Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page
Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage
Simon Thomas website
Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page
Joel Lebowitz, Michael Kiessling
Yanyan Li, Haim Brezis Organizer's Webpage
Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website
Stephen D. Miller
Brooke Ogrodnik, Website
Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum
Yael Davidov Seminar webpage
Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page
Fioralba Cakoni Seminar webpage
Ebru Toprak, Organizer
Organizer's webpage: Organizer's webpage
- Show events from all categories
Special Note to All Travelers
Directions: map and driving directions. If you need information on public transportation, you may want to check the New Jersey Transit page.
Unfortunately, cancellations do occur from time to time. Feel free to call our department: 848-445-6969 before embarking on your journey. Thank you.