Model Theory of a Hilbert Space Expanded with an Unbounded Closed Selfadjoint Operator
Logic
2011-06-07 v5 Spectral Theory
Abstract
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.
Cite
@article{arxiv.1102.2454,
title = {Model Theory of a Hilbert Space Expanded with an Unbounded Closed Selfadjoint Operator},
author = {Camilo Argoty},
journal= {arXiv preprint arXiv:1102.2454},
year = {2011}
}