Mathematical Sciences: Research in Model Theory: Strongly Minimal Fusions and Other Homogeneous-Universal Models

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9510377 Holland Holland's research is in model theory, a branch of mathematical logic. In recent years, many new structures of interest to model theorists have been constructed as homogeneous-universal models for classes of finite models with a notion of dimension. Among these new structures are the new strongly minimal structures built from existing ones by the method of fusion introduced by Hrushovski. Holland has begun a general, systematic study of arbitrary fusions from a geometric point of view. The new perspective gained therefrom enabled Holland to produce a simple, more transparent construction than that of Hrushovski in a particular case. She intends fully to generalize the simplification and to continue the systematic study of fusions both from a geometric point of view, to see what new information the provide on the classification of geometries that arise from strongly minimal structures, and from a model theoretic point of view, to see whether variations on the strongly minimal construction might provide further examples of model theoretic interest. In parallel, Holland intends to work toward a unified framework in which to view all of the new work on homogeneous-universal models. Holland intends to use the planning period to refine her research project, formulating the specific, plausible conjectures that should constitute a credible NSF proposal. ***