Cummings and Schimmerling propose an innovative series of workshops on set theory for the Appalachian region. Each workshop would be devoted to a single topic such as a broadly applicable method, a complex seminal paper or a significant unpublished theorem. The topic for each workshop would be announced several months in advance together with suggested background reading material. The immediate goal would be for faculty and students who are not experts in the topic to get to the point where they could start to use its techniques in one or two intensive days. Each time, an expert in the topic would be asked to lead the workshop, which could mean doing all the lecturing herself or himself, or delegating parts to others. There would be three workshops per calendar year; students would be paid to generate notes for the participants, which might also be disseminated in print or on the web. Special emphasis would be given to encouraging the participation of mathematicians from underrepresented groups.
Set theory is the study of infinite structures; among the principal objects of study are infinite sets, graphs, trees, games and orderings. What gives the subject its distinctive flavour is the heavy use of tools from mathematical logic, which are used side-by-side with the "combinatorial" methods familiar from the study of finite structures. Ideas from set theory have found application in many areas of mathematics: to pick a recent example Gowers' celebrated work in analysis uses the ideas of some classical work on colourings of infinite families of infinite sets.
