LOGIC
IN
SOUTHERN CALIFORNIA
Saturday, February 23, 2013
Rowland Hall 306
Funded by NSF Grant DMS-1044150
Schedule:
2:00 - 3:00 Trevor Wilson (UCI)
3:30 - 4:30 Robin Tucker-Drob (Caltech)
5:00 - 6:00 Ryan Holben (UCI)
Abstracts Driving directions and parking Organizers Previous meetings
Trevor Wilson: Scales
on Pi^2_1 sets
Abstract: Scales are used in descriptive set theory as a
way to uniformize sets in the plane, often in the context of the
Axiom of Determinacy (AD) or its natural strengthening AD^+.
Although AD contradicts the Axiom of Choice, uniformization
principles can be considered as weak forms of choice and so their
co-existence with AD is a rather subtle issue. A well-known
theorem of Woodin gives scales on Sigma^2_1 sets. The
natural next step is the construction of scales on Pi^2_1 sets,
which requires some additional hypothesis beyond AD^+. We
discuss existing results and then present a method to produce a
scale of optimal complexity---namely, the norms of the scale are
definable from ordinals.
Robin Tucker-Drob: Shift-minimal groups and cost
Abstract:
A countable group G is called shift-minimal if all non-trivial
measure preserving actions weakly contained in the Bernoulli shift
of G are free. I will discuss the connection between
shift-minimality, cost, and certain properties of the reduced
C*-algebra of G, indicating the proof that if a countable group G
admits a free measure preserving action of cost strictly greater
than 1 then there is a finite normal subgroup N of G such that G/N
is shift-minimal. This implies shift-minimality for a wide variety
of groups including all non-abelian free groups. I will also
discuss a number of open questions related to shift-minimality and
cost.
Ryan Holben: Square at
Singular Cardinals
Abstract: Square principles refer to a family of
infinitary combinatorial principles which are studied in set
theory. Square is intimately related to a number of other
principles such as the tree property and stationary set
reflection. Finding the consistency strength of these principles
at small singular cardinals is an interesting and difficult
problem which relates to the Singular Cardinal Hypothesis. We look
at some classical theorems which tie these results together, then
introduce some of our own results and discuss the methods needed.
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