A Model Existence Theorem for Infinitary Formulas in Metric Spaces
arXiv:math/9802114
Abstract
We prove a Model Existence Theorem for a fully infinitary logic for metric structures. This result is based on a generalization of the notions of approximate formulas and approximate truth in normed structures introduced by Henson and studied in different forms by Anderson and Fajardo & Keisler. This theorem extends Henson's Compactness Theorem for approximate truth in normed space structures to infinitary formulas.
26 pages. See also http://www.beaver.edu/programs/math%26compsci/ortiz.htm