Mathematical Sciences: Geometrical Stability Theory
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Steven A. Buechler's research project is in stability theory,              a subfield of model theory.  In recent years several general model-             theoretic problems have been systematically approached via the                  stability hierarchy.  Even though the problem itself may not                    involve stability-theoretic notions, considering separately the                 cases:  omega-stable, superstable, etc., brings into play a mass of             technical machinery.  Such is the case with Vaught's conjecture,                which was proved by Shelah for omega-stable theories.  The next                 step is to consider all superstable theories, but this has proven               to be too difficult.  Buechler will approach this problem by                    separating the superstable theories according to their                          "geometrical" properties.  The first case to consider is when the               universe has Shelah rank 1.  Buechler has already made progress on              this problem.
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