Vol. 23, No. 2, 1967

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Application of infinitary languages to metric spaces

Ralph David Kopperman

Vol. 23 (1967), No. 2, 299–310

We attempt to lay the groundwork for applying the recently-developed theory of models for the infinitary languages Lπ𝜖t to analysis. It will be shown that within one of these languages, axioms may be written whose class of models is precisely the metric spaces. We show that two complete separable metric spaces are elementarily equivalent in this language if and only if they are isomorphic and obtain an elimination of quantifiers for such spaces. A method is developed for transferring results on metric spaces to structures with metrics whose relations are closed under the metric topology. This class includes Banach Spaces.

Mathematical Subject Classification
Primary: 02.35
Received: 20 April 1966
Published: 1 November 1967
Ralph David Kopperman