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 Driving directions and parking Organizers Participants Previous meetings
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