LOGIC
IN
SOUTHERN CALIFORNIA
Saturday, May 10, 2014
Rowland Hall 306
Funded by NSF Grant DMS-1044150
Schedule:
2:00 - 3:00 Sherwood
Hachtman (UCLA)
3:30 - 4:30 Bill Chen
(UCLA)
5:00 - 6:00 Monroe Eskew
(UCI)
Abstracts Driving directions and parking Organizers Previous meetings
Bill Chen: Tight
stationarity and careful sets
Mutual stationarity is a notion of stationarity for certain
sequences of subsets of a singular cardinal $\lambda$ (possibly
even of countable cofinality) which was defined by Foreman and
Magidor. They isolated tight stationarity as a
version of mutual stationarity that is easier to
analyze. We use a pcf-theoretic scale to relate sequences of
subsets of $\lambda$ to subsets of $\lambda^+$, translating
from tightly stationary sequences to stationary subsets of
$\lambda^+$. Then we will define careful sets, which are the
subsets of $\lambda^+$ that are involved in this translation. The
main result is the construction of a model where $\lambda$ is a
strong limit and every subset of $\lambda^+$ is careful. This
construction uses the combinatorics of tree-like scales and a
diagonal supercompact Prikry forcing.
Monroe Eskew:
Applications of the anonymous collapse
Abstract: We will discuss a "universal" forcing for collapsing a
large cardinal to be the successor of smaller regular
cardinal. It absorbs most of the effects of a wide class of
"standard" collapsing posets, yet is incomparable with all of
them, hence the name, anonymous collapse. Using this forcing, we
show how to construct many different models with the same reals
and same cardinals but very different cardinal characteristics of
the continuum. We show how it can be used with almost-huge
cardinals to achieve minimal solutions to Ulam's measure problem,
and to obtain successor cardinals which are "generically
supercompact" in a strong sense. This will enable a solution
to a question of Foreman related to an old conjecture in model
theory about the cardinality of ultrapowers. In contrast to
the traditional variety, we show that these generically
supercompact cardinals are compatible with squares.
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. There are very few visitor parking slots in lot 12 as well, they are next to the pay machines. So you may also park there, but these spots are hard to get -- they are usually taken. 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, Matthew Foreman, Martin Zeman
Local organizers: Matthew Foreman, Martin Zeman