Saturday, November 14, 2015

Rowland Hall 306

Funded by NSF Grant DMS-1044150


2:00 - 3:00  James Freitag (UCLA)

3:30 - 4:30  William Chan (Caltech)

5:00 - 6:00  Nam Trang (UCI)

Abstracts    Driving directions and parking    Organizers   Participants   Previous meetings  

Abstracts of the talks:  

James Freitag:   The finite cover property

Abstract: We will explain the finite cover property (FCP), a property of first order formulas and also of theories. The original definition is due to Keisler, who investigated the property in the context of saturation of ultrapowers. The property is interesting in its own right, and was later investigated in a variety of contexts by Shelah. Establishing the negation of the FCP (NFCP) for specific theories is often useful for applications, and we will prove the theory of algebraically closed fields has NFCP. In many circumstances, establishing effective versions of the NFCP, is also of great interest. We will explain the recently proved effective NFCP proved for differential fields, along with applications.

William Chan:  Equivalence Relations which are Borel Somewhere     

Abstract: In this talk we will discuss circumstances under which certain analytic equivalence relations can become Borel when restricted to non-trivial sets according to appropriate sigma-ideals on Polish spaces.

Nam Trang:  Large cardinals, determinacy, and forcing axioms

Abstract:We discuss some recent progress in descriptive inner model theory. In particular, we discuss some current results concerning connections of the three hierarchies of models: canonical models of large cardinals (pure extender models), canonical models of determinacy, and strategic hybrid models (e.g. HOD of determinacy models). These structural results can be used to improve (lower-bound) consistency strength of strong combinatorial principles such as PFA, strong forms of the tree property etc. In particular, I proved that PFA implies the existence of a transitive model of ``AD_R + Theta is regular". Building on this and structural results above, G. Sargsyan and I have constructed models of theory LSA =_{def} "AD^+ + there is an \alpha such that Theta=\theta_{\alpha+1} + \theta_\alpha is the largest Suslin cardinal" from PFA. This result is the strongest of its kind and reflects our current understanding of HOD of models of determinacy.

Driving directions and parking: 

For maps, and other travel information click here. Rowland Hall is building 400 on the map.

From the north:

From the south:

To park on campus you will need to purchase a parking permit. You can buy a parking permit from the dispenser near the entrance to lot 16. Park in lot 16. Parking may cost as much as $14 for the full day. That kiosk takes both cash and credit cards. Quarterly or annual parking permits from other UC campuses are honored at UCI (more information on parking permit reciprocity is available here).

Organizers:  Alexander Kechris, Itay Neeman, Martin Zeman 

Local organizer: Martin Zeman 

Caltech: Alexander Kechris, William Chan, Ronnie Chen, Connor Meehan 
UC Berkeley: Nick Ramsey  
Donald Martin, Itay Neeman, Artem Chernikov, James Freitag, Alex Mennen, Omar Ben Neria, John Susice
UCI: Martin Zeman, Nam Trang, Garrett Ervin, Geoff Galgon, Curtis Koch, Kameran Kolahi, Jeffrey Schatz, Ryan Sullivant, Trevor White
Furman University, SC: Ryan Holben

Previous meetings:         

Caltech, March 7, 2015    

UCLA, November 15, 2014     

UCI, May 10, 2014     

Caltech, March 8, 2014      

UCLA, November 16, 2013     

UCLA, June 1, 2013     

UCI, February 23, 2013     

Caltech, November 17, 2012

UCLA, May 12, 2012

Caltech, February 18, 2012

UCI December 3, 2011