LOGIC IN SOUTHERN CALIFORNIA

Saturday, November 14, 2015

Rowland Hall 306

Funded by NSF Grant DMS-1044150

Schedule:

2:00 - 3:00  James Freitag (UCLA)

3:30 - 4:30  William Chan (Caltech)

5:00 - 6:00  Nam Trang (UCI)

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:

• Take I-405 to 73 south. Exit at Bison. (Bison is the last toll-free exit!!!)

• Turn left onto Bison.

• Pass East/West Peltason and continue straight ahead to lot 16.

From the south:

• Take I-5 to 73 north, and exit 73 at Bison (toll).

• Turn right onto Bison.

• Pass East/West Peltason and continue straight ahead to lot 16.

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

Participants:
Caltech: Alexander Kechris, William Chan, Ronnie Chen, Connor Meehan
UC Berkeley: Nick Ramsey
UCLA:
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:

UCI December 3, 2011