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# Program for Saturday

Christian Rosendal, University of Illinois at Chicago.

** Hour: ** 9:00 - 10:00

** Title: ** Large scale geometry of metrisable groups.

** Abstract: ** Large scale geometry of finitely generated or locally compact groups has long been one of the cornerstones of geometric group theory and its connections with harmonic and functional analysis. However, many of the groups of interest in logic, topology and analysis fail to be locally compact, such as automorphism groups of countable structures, diffeomorphism and isometry groups. For these there has been no canonical way of defining their large scale structure, as it is possible, e.g., with the word metric on a finitely generated group. Moreover, recently many groups have turned out to have no non-trivial large scale structure at all, despite being non-compact. We present a theory of large scale structure of metrisable groups and among other things determine the necessary and sufficient conditions for this structure to be unique up to coarse or quasi-isometric equivalences. Applications to model theory will be presented.

Mirna Džamonja, University of East Anglia, Norwich.

** Hour: ** 10:20 - 11:20

** Title: ** Would Mostowski have liked it?

** Abstract: ** We shall speak of some points of interest in set theory and applications over the last years and overlaps of this with model theory and foundations

Sławomir Solecki, University of Illinois at Urbana-Champaign.

** Hour: ** 11:30 - 12:30

** Title: ** General approach to finite Ramsey theory and a new Ramsey theorem.

** Abstract: ** In recent years, finite Ramsey theorems have been used in studying dynamics of groups of
interest to Model Theorists and Descriptive Set Theorists. I will present a general approach to finite
Ramsey theory, which reveals the formal algebraic structure underlying results of that theory. Most
concrete unstructured finite Ramsey results turn out to be special instances of the main theorem of this
general theory. I will also describe a very recent concrete Ramsey result—dual Ramsey theorem for
trees—which was obtained using the general theory. This result was partly inspired by the internal logic
of the theory and partly by considerations related to amenability of groups.

Zlil Sela, Hebrew University, Jerusalem.

** Hour: ** 14:30 - 15:30

** Title: ** Low dimensional topology and the elementary theory of groups.

** Abstract: ** We will survey some results on the first order theory of
free and free products of groups, and indicate concepts and
techniques from low dimensional topology that play an essential role
in proving, and at times even stating, some of these results.

These will include Tarski's problem on the elementary equivalence of non-abelian free groups, and Vaught-Malcev problem on the elementary equivalence of free products of pairs of elementarily equivalent groups, as well as other results on the structure of definable sets in related theories. We will assume no prior knowledge in model theory nor in low dimensional topology.

Jan Woleński, Jagiellonian University.

** Hour: ** 15:50 - 16:50

** Title: ** Tarski, Mostowski and philosophy (not only of mathematics).

** Abstract: ** The Warsaw logical milieu in the interwar period was compact as far as the issue concerns the
basic direction of research and views about logic and its tasks, but it consisted of philosophers
(Leśniewski and Łukasiewicz as the main figures) and mathematicians (Tarski, Lindenbaum
and Mostowski as leading persons). This division is fuzzy to some extent, because all
Warsaw logicians shared interests in philosophy and were ready to discuss philosophical
problems not necessarily belonging to philosophy of mathematics. Yet almost all members of
this group (Lesniewski was an exception in this respect) considered logic as independent of
philosophy. In particular, formal logical investigations and results should not be limited by
philosophical presuppositions or prejudices. On the other hand, philosophical inspiration for
logic was welcomed. Both Tarski and Mostowski represented this attitude in a particularly
paradigmatic manner. Since their philosophical remarks were short and not numerous, it
is possible to reconstruct their more general philosophical views. For example, both were
inclined to empiricism as an epistemological position and favored conceptualism and even
nominalism (Tarski) as an ontological view about the existence of mathematical objects. The
paper is devoted to looking for other philosophical ideas possibly present in works of Tarski
and Mostowski.

Rump Session.

Johann A. Makowsky, Technion, Haifa.

** Hour: ** 21:00 - 22:00

** Title: ** Andrzej Mostowski, the man and his legacy.

** Abstract: ** I will try to remember A. Mostowski, the human being, the scholar, the bridge builder, and his legacy, both in the context of the Cold War and from a personal perspective.