The goal of European Set Theory Meetings is to bring together most active researchers in this subject from Europe with the goal of creating a European network in set theory. While the meeting will be European in character it will be open and we plan to invite a number of leading experts in the field from the US and other parts of the world. Particular emphasis will be given to supporting young European graduate students and postdocs. Poland was selected as the host of this meeting since researchers from Poland have played a special role in its development from the early days of the subject. In particular, we hope that a number of Polish and other European mathematicians working outside of Europe will be able to attend and thus strengthen their ties with the scientists working in Europe. This current meeting will be the second in this series. The first meeting took place in Bedlewo July 9 to 13, 2007 and has attracted over 80 mathematicians, among them some of the leaders in this subject.
The scientific topics of the meeting will cover the three principal areas of set theory.
The first topic is foundations of mathematics. While the usual axioms ZFC of set theory are sufficient for most of mathematics, it is well that they are incomplete and in particular do not decide some of the basic questions of set theory such as the Continuum Hypothesis as well as its generalizations and variations. Set theorists have been searching for natural extensions of these axioms which would decide these open problems. There are two basic types of additional axioms which are considered: large cardinal axioms, which postulate that the set theoretic universe is “tall”, and forcing axioms which postulate a certain form of saturation of the set theoretic universe. Both of these directions reinforce Gödel’s basic intuition that additional axioms of set theory should be certain forms of maximality principles.
The second direction is descriptive set theory which studies properties of definable sets of reals, and more generally Polish spaces. In recent years a number of important developments have brought descriptive set theory closer to ergodic theory, dynamical systems and the theory of group representations. This connections is achieved through the study of orbit equivalence relations and the corresponding quotient spaces. While these spaces are singular, i.e. the Borel structure on them is degenerate, it is possible to study their properties by lifting them to the original space.
Finally, combinatorial set theory deals with uncountable structures without any definability restrictions. Most of the questions in this area are independent of ZFC and their study requires the use of Cohen’s method of forcing. In recent years, remarkable results have been obtained in this area and some of the most outstanding open problems have been solved.
We intend to have two mini courses by prominent researchers, one from “pure” set theory and one at the interface of set theory and some other area of mathematics such as Banach space theory. In addition, we will have around 20-25 lectures of 30-50 min each. The total number of participants is expected to be around 60-80. The meeting will take place July 6-10, 2009 at the Mathematical Research and Conference Center, Będlewo Poland.
For the program and all further information please visit www.esf.org/conferences/09306 . Note that the closing date for applications is April 8 2009.