Description and aim
Set theory grew out of mathematical analysis through Georg Cantor's work
on sets of uniquness of trigonometric series in the late 19 th century. Over the last
century it has developed into a vibrant and important subject of its own. On one hand it
deals with questions of deep foundational impotance, such as the choice of axioms for
mathematics and the questions of relative consistency of mathematical theories.
On the other hand, techniques of combinatorial set theory can be applied successfully in
a number of different areas of mathematics such as: general topology, measure theory,
Banach space theory, abstract algebra, while descriptive set theory is applied in ergodic
theory, dinamical systems, group representation theory, etc.
In the early days of set theory most of the advances were made in Europe. In particular, Polish mathematicians such as Sierpinski, Kuratowski, Mostowski and others played a key role in the early development of the subject. Among other things, they created the journal Fundamenta Mathematicae which published some of the main early papers in set theory and was the primary reference in the subject. In 1939 Alfred Tarski moved from Poland to the US and later created the logic group in Berkeley which became the strongest center in mathematical logic and set theory in the world. While set theory continued to be practiced in Europe, it is fair to say that starting from Paul Cohen’s invention of the method of forcing in 1963 the center of gravity moved to the US. However, in the last ten years or so, a number of strong researcher groups in set theory were created in Europe (Barcelona, Helsinki, Paris, Vienna, etc).
The goal of this meeting is to bring these groups together with the idea of later 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. Thus, we hope that a number of Polish and other European set theorist working abroad will be able to attend and thus strengthen their ties with the scientists working in Europe. Particular emphasis will be given to supporting young Euroepan graduate students and postdocs.
- Inner model theory and large cardinals
In particular, we plan to discuss the work of Woodin on Omega-logic and its implications for the Continuum Hypothesis and other problems of set theory undecidable on the basis of the usual axioms ZFC.
- Descriptive set theory
We intend to cover recent exciting progres on classification problems and definable equivalence relations, the work of Kechris, Hjorth, Solecki and others in this area.
- Combinatorial set theory and applications to Banach spaces, measure theory, general topology