arXiv:1102.2454 Abstract | arXiv Analytics

arXiv:1102.2454 [math.LO]Abstract References Reviews Resources

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

Published 2011-02-11, updated 2011-06-06Version 5

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.

Categories: math.LO, math.SP

Subjects: 03C45, 03C48, 03C52, 03C65, 03C98, 28E15, 37K05, 46C05, 46C07, 47A05

Keywords: unbounded closed selfadjoint operator, hilbert space, model theory, metric abstract elementary classes, superstable first order theorues

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