Abstract

BERENSTEIN, Alexander; HYTTINEN, Tapani  and  VILLAVECES, Andrés. Hilbert spaces with generic predicates. Rev.colomb.mat. [online]. 2018, vol.52, n.1, pp.107-130. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v1n52.74566.

We study the model theory of expansions of Hilbert spaces by generic predicates. We first prove the existence of model companions for generic expansions of Hilbert spaces in the form of a distance function to a random substructure, then a distance to a random subset. The theory obtained with the random substructure is (-stable, while the one obtained with the distance to a random subset is TP 2 and NSOP 1. That example is the first continuous structure in that class.

Keywords : Continuous logic; Random Predicates; TP ₂; Stability theory.

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