Mathematical Sciences: Recursive Model Theory
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Knight is continuing her work in recursive model theory.                Over the past two years, she has obtained several results on                    degrees of models realizing prescribed sets of bounded complexity               types (finitary or infinitary).  The problem of characterizing                  the degrees of isomorphic copies of a given model now seems                     approachable.  Knight and Slaman have a characterization for                    models of finite Scott height.  The characterization is                         unpleasantly complicated, and they hope to simplify it.  The                    recent results use a powerful method of Harrington.  In addition                to using the method to obtain further results, Knight hopes to                  come to a better understanding of the method itself.  Ash                       developed a related method and proved a theorem giving general                  conditions under which his method works.  Ash and Knight have                   begun trying to compare the two methods.  All of these                          investigations shed further light on the theoretical limits of                  computing power, a matter that becomes increasingly relevant and                fascinating as the actual limits of computing power expand with                 each generation of new machines.
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