Singular Cardinal Combinatorics

From May 1 to May 6, 2004 24 set theorists met at the Banff International Research Station to discuss Singular Cardinal Combinatorics. Descriptions of the contents of their talks will be published in a Proceedings that will appear in the Notre Dame Journal of Symbolic Logic. During the workshop, several important new results were announced and explained, and there were problem sessions held (some with significant amounts of prize money attached to particular problems, see the last section for details). To summarize the direction of the conference we will present here an annotated collection of representative problems with some references. Where the problems were novel, attribution is attempted and it is noted where there is money attached to particular problems. Three closely related themes dominated the discussion: stationary sets and stationary set reflection, variations of square and approachability and the singular cardinals hypothesis. Underlying most of the discussion were ideas from Shelah’s PCF theory. Important subthemes were mutual stationarity, Aronszajn trees and superatomic Boolean Algebras.