Appalachian set theory
Appalachian set theory
Saturday, May 31, 2008
9:30 a.m. - 6 p.m. with coffee and lunch breaks
Penn State University
114 McAllister "the math building" (Campus maps)
Justin Moore : "Set mapping reflection"
Description
The subject of this tutorial will be the Set Mapping Reflection
Principle. This is a newly isolated consequence of the Proper Forcing
Axiom which has a strong influence on the filter of closed unbounded
subsets of &omega1. It has proved useful in a number of seemingly
different contexts: the study of Aronszajn trees and lines, the
computation of the exponential function at singular cardinals, and the
existence of definable well orderings of the reals.
The tutorial will begin with a review of some of the fundamental
definitions: the closed unbounded filter of countable subsets of a given
set, stationary sets, elementary submodels. I will give a proof that
PFA implies MRP and that MRP implies that the continuum is the second
uncountable cardinal. I will also include some other "warming up"
examples. The remainder of the tutorial will examine some more involved
examples and list some open problems.
Suggested reading
-
J. Tatch Moore, Set mapping reflection, Journal of Mathematical
Logic 5 (2005) 87-98
[Link]
-
B. Koenig, P. Larson, J. Tatch Moore and B. Velickovic, Bounding the
consistency strength of a five element linear basis, to appear in
Israel Journal of Mathematics
[Link]
-
M. Viale,
A family of covering properties, Mathematical Research Letters, 2008,
volume 15, no. 2, 221--238
[Link]
Local information
Lodging is a serious issue near Penn State so please make your reservations
right away.
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A block of rooms will be held until May 1 at the recommended hotel:
Days Inn Penn State
(mention Appalachian set theory when making your reservation)
$85 / night + tax
240 S. Pugh Street
(814) 238 - 8454
(800) 258 - 3297
(If you get transfered to the national reservation center, try again.
You need to speak to a person at the hotel itself.)
http://www.lioncountrylodging.com/
-
A block of rooms will be held until May 16 at:
Sleep Inn of State College
(mention Appalachian set theory when making your reservation)
$75 / night + tax
111 Village Dr.
(814) 235 - 1020
-
The Penn State Visitor's Guide is at
http://www.psu.edu/ur/visitors.html
-
The closest airport is
University Park Airport (SCE).
Participant travel support
Funds provided by the National Science Foundation will be used
to reimburse some participant transportation and lodging expenses.
Priority will be given to students
and faculty who do not hold federal research grants.
Please request such funds as far in advance of the meeting as possible
by sending the following information to
James Cummings and
Ernest Schimmerling by email.
- Your name, university affiliation,
mailing address, phone number and email address
- Your professional status and
- undergraduate students: please describe your background in set theory
- graduate students: please tell us your year and the name of
your thesis advisor if you have one
- faculty: please tell us whether you hold a federal research grant
- A brief statement about your interest in the workshop