Multimetric continuous model theory

In this paper, we study metric structures with a nite number of metrics by extending the model theory developed by Ben Yaacov et al. in the monograph Model theory for metric structures. We rst de ne a metric structure with nitely 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