Submission date: 13 April 2007

Abstract:

We prove the existence of model companions for three kinds of generic expansions of Hilbert spaces: first we add a distance function to a random substructure, then a distance to a random subset and finally a random predicate. The theory obtained with the random substructure is omega-stable, while those obtained with the distance to a random subset and the random predicate are unstable. In addition to providing these model companions, we start the model theoretic study of these generic expansions.

Mathematics Subject Classification: 03C10, 03C30

Keywords and phrases: continuous model theory, existentially closed structures, generic expansions

Full text: (arXiv) pdf, ps.