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.

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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

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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.

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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.

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