Multimetric continuous model theory
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2012
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University of Hawaii at Manoa
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In this paper, we study metric structures with a finite number of metrics by extending the model theory developed by Ben Yaacov et al. in themonograph Model theory for metric structures. We first define a metric structure with finitely many metrics, develop the theory of ultraproducts of multimetric structures, and prove some classical model-theoretic theorems about saturation for structures with multiple metrics. Next, we give a characterization of axiomatizability of certain classes of multimetric structures. Finally, we discuss potential avenues of research regarding structures with multiple metrics.
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Plan B paper, M.A., Mathematics, University of Hawaii at Manoa, 2012
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28 pages
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