Hilbert Spaces with Generic Predicates

Details Hilbert Spaces with Generic Predicates Hilbert Spaces with Generic Predicates

2007-04-12

arxiv.org/abs/0704.1633v1

Mathematics

Logic

29 pages

Scientific paper

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.

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