15 research outputs found
A presentation theorem for continuous logic and Metric Abstract Elementary Classes
We give a presentation theorem for continuous first-order logic and Metric
Abstract Elementary classes in terms of and Abstract
Elementary Classes, respectively. This presentation is accomplished by
analyzing dense subsets that are closed under functions. We extend this
correspondence to types and saturation
Tameness in generalized metric structures
We broaden the framework of metric abstract elementary classes (mAECs) in
several essential ways, chiefly by allowing the metric to take values in a
well-behaved quantale. As a proof of concept we show that the result of Boney
and Zambrano on (metric) tameness under a large cardinal assumption holds in
this more general context. We briefly consider a further generalization to
partial metric spaces, and hint at connections to classes of fuzzy structures,
and structures on sheaves