Stability Theoretic Methods in Unstable Theories (09w5113)

Arriving in Banff, Alberta Sunday, February 8 and departing Friday February 13, 2009


Bradd Hart (McMaster University)

Alf Onshuus (Universidad de los Andes, Edificio H)

Anand Pillay (University of Leeds)

(University of California at Berkeley)

(Université Claude Bernard Lyon 1)


The general aim is to apply methods originating in stability theory to unstable theories, and find applications in model theory and other parts of mathematics.

This has already been an important theme over the past 25 years, with o-minimality, smoothly approximable structures, and simple theories being key examples.

But there have been some key recent developments which bring new ideas and techniques to the table. One of these is the investigation of abstract notions of independence, leading to the notions of thorn forking and rosiness. Another is the discovery that forking, weight, and related notions from stability are meaningful in theories without the independence property. Another is the formulation of notions of stable, compact, or more general domination, coming from the analysis of theories such as algebraically closed valued fields and o-minimal theories. One more is the fast development of "continuous" model theory, which provides more flexible notions of definability.

The (overlapping) themes of the meeting will include:

(i) The classification of first order theories (and also continuous theories): identifying meaningful dividing lines, properties (rosiness, independence property, strict order property, SOP_n, variations of the tree property, strong dependence, various notions of minimality including dp-minimality).

(ii) Use of stability-style techniques in some of the "good" classes of theories from (i). This includes forking and weight, dp-rank and thorn rank, meta-analysability, definable types, stable domination, compact domination, Keisler measures.

(iii) Use of the above techniques to help classify or describe models of "nice" unstable theories, and algebraic structures, such as groups and fields, which are definable in "nice" unstable theories.

We plan to include survey or expository talks, research talks, and leave sufficient time for informal work and discussion.