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

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

2011-02-11

arxiv.org/abs/1102.2454v5

Mathematics

Logic

Scientific paper

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.

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