Research Interests

Model theory broadly construed. My current research focuses primarily on three topics. First the model theory of ordered structures, here the program is to investigate ordered structures with "well-behaved" model theory in contexts more general than o-minimality. Representative work is on theories of o-minimal open core as well as theories associated to planar vector fields. Currently I am trying to broaden the scope of these investigations to include general topological theories, particularly those built upon p-adic fields. My second area of focus is on trivial uncountably categorical theories. Here the major program is to prove that such a theory admits an axiomatization of bounded quantifier depth. Lastly I am interested in classification problems for theories at a level more general than simplicity. Here the program, following Shelah, is to find classes of theories in which the existence of universal models is more robust then would be expected in general.

Some Publications and Preprints

(With Patrick Speissegger) "An Ordered Structure of Rank Two Related to Dulac's Problem". PDF (Shows the existence of a model theoretic structure associated to the flow of vector field in the plane. Demonstrates how qualitative aspects of the flow are reflected in the model theory of the structure.)

"A Note on Weakly O-Minimal Structures and Definable Completeness", to appear Notre Dame Journal of Formal Logic. PDF (Shows certain desirable topological properties of o-minimal structures do not persist in the weakly o-minimal setting. Constructs an example to show that in the absence of definable completeness there are structures with a host of good model theoretic properties which are nonetheless not "close" to weakly o-minimal.)

(With M.C. Laskowski and A. Raichev) "Model Completeness for trivial, uncountably categorical theories of Morley Rank 1", Archive for Mathematical Logic (2006),45:931-945. PDF(We prove that a trivial uncountably categorical theory of Morley rank 1 is model complete after naming constants for a model.)

"Forking and Independence in O-Minimal Theories", Journal of Symbolic Logic,(2004),69:215-240 (Gives a "natural" description of forking in o-minimal theories.)

"Weak Dividing, Chain Conditions, and Simplicity", Archive for Mathematical Logic, (2004),43:265-283.(Investigates simplicity for the point of view of weak dividing.)