Combinatorial set theory and forcing theory

The combinatorial investigation of infinite sets goes back to Cantor and received a major impetus through Cohen's invention of forcing. It soon turned out that the forcing method was useful not only for dealing with problems in combinatorial set theory like cardinal arithmetic, but also for solving problems from other areas of mathematics like Suslin's hypothesis or the Whitehead problem. In set theory proper, forcing plays a major role in the study of both small sets (e.g., the combinatorial investigation of sets of reals, cardinal invariants of the continuum, etc.) and large sets (e.g., $P_\kappa \lambda$ combinatorics, large cardinal axioms, etc.). Recently, the techniques of combinatorial set theory and forcing theory have considerably grown in depth, and old problems have been solved with sophisticated methods. Examples are Moore's proof of the existence of an L-space using minimal walks, and Farah's result saying that under the open coloring axiom OCA, the Calkin algebra has only inner automorphisms.

The topic of this meeting is recent developments in combinatorial set theory and in forcing theory as well as in their applications to other areas of mathematics. Its goal is to bring together researchers in these areas from Japan and abroad and to foster academic exchange. The program will feature two minicourses (by Sy Friedman and by Ilijas Farah). Additionally, we expect many talks, in particular by junior participants, both from Japan and abroad.

Since several set theorists from abroad will visit Japan in November, we anticipate additional research activities like minicourses and seminar talks in the week preceding the workshop and/or the week following the workshop, at either Nagoya University or Kobe University. Details have not been settled yet.

The second half of November is one of the best times to visit Kyoto, Japan's ancient capital, because of the leaves turning red and yellow in the temple gardens bordering the city. Unfortunately, this also means that the time of the workshop is high season, and hotel reservations should be made as early as possible.

Proceedings of the workshop is available (RIMS website).

Prospective participants should contact either the organizer, Teruyuki Yorioka, or Jörg Brendle, as early as possible.