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"

List of participants in this workshop

Lecture notes by Justin Moore and David Milovich


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

Local information

Lodging is a serious issue near Penn State so please make your reservations right away.

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.