Model Theory of a Hilbert Space Expanded with an Unbounded Closed Selfadjoint Operator

Camilo Argoty

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arxiv 1102.2454 v5 pith:FO2QCR5M submitted 2011-02-11 math.LO math.SP

Model Theory of a Hilbert Space Expanded with an Unbounded Closed Selfadjoint Operator

Camilo Argoty This is my paper

classification math.LO math.SP

keywords characterizeclosedhilbertmaecoperatorspaceunboundedabstract

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We study a closed unbounded self-adoint operator Q acting on a Hilbert space H in the framework of Metric Abstract Elementary Classes (MAECS). We build a suitable MAEC for (H,Q), prove it is aleph 0 stable up to perturbations and characterize non-splitting and show it has the same properties as non-forking in superstable first order theorues. Also, we characterize equality, orthogonality and domination of (Galois) types in that MAEC.

Model Theory of a Hilbert Space Expanded with an Unbounded Closed Selfadjoint Operator

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