Model theory of a non-degenerate representation of a unital C*-algebra

Details Model theory of a non-degenerate representation of a unital C*-algebra Model theory of a non-degenerate representation of a unital C*-algebra

2010-10-29

arxiv.org/abs/1010.6188v2

Mathematics

Logic

Scientific paper

We study the theory of a Hilbert space H as a module for a unital C*-algebra A from the point of view of continuous logic. We show this theory, in an suitable language, has quantifier elimination and it is superstable. We show that for every v in H, the type of v over the empty set is in correspondence with the positive linear functional over A defined by v. Finally, we characterize forking, orthogonality and domination of types and show the theory has weak elimination of imaginaries.

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