Kyoto, Japan

Large cardinals play important roles in modern set theory. By the development of forcing theory and inner model theory, many set theoretical propositions, even statements about relatively small cardinals, turned out to have the same consistency strength as some large cardinal axioms. Now large cardinal axioms are recognized as the measure of consistency strength of set theoretical propositions. It is also known that large cardinal axioms determines most of the classical problems on descriptive set theory. These results can be applied to many other areas of mathematics such as general topology, infinite graph theory, etc.

The topic of this meeting are recent developments on the interplay between large cardinals and mathematical objects of relatively small cardinalities. Its goal is to bring together researchers in set theory from Japan and abroad and to foster academic exchange. The program will feature two minicourses by Matthew Foreman and by Lajos Soukup:

## Minicourses

- Matthew Foreman (University of California, Irvine)
- Lajos Soukup (Hungarian Academy of Sciences)
We expect many talks, in particular by junior participants, both from Japan and abroad.

Prospective participants should contact the organizer, Hiroshi Sakai, as early as possible.This workshop is in a series of workshops held in Japan every year supported by Research Institute for Mathematical Sciences (RIMS). Here are web pages of the past two years:

- Dates:

October 25 - 28, 2010- Venue:

Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan- Organizer:

Hiroshi Sakai (Kobe University) E-mail: