Maximality of continuous logic
Xavier Caicedo · 2017
The analogue of Lindstrpom’s characterization of elementary logic in terms of compactness and the downward Lowenheim-Skolem theorem is shown for continuous logic, introduced originally for Banach spaces by Henson and Iovino as a logic of approximate satisfaction and generalized later to metric spaces by Ben Yaacov and Usvyatsov. For this purpose we characterize equivalence of models in this logic by means of partial approximations and identify some useful properties of its compact extensions.