Model theory of a Hilbert space expanded with an unbounded closed selfadjoint operator

摘要

We study a closed unbounded self-adjoint operator Q acting on a Hilbert space H in the framework of Metric Abstract Elementary Classes (MAECs).We build a suitableMAEC for such a structure, prove it is ?_0-categorical and ?_0-stable up to a system of perturbations.We give an explicit continuous L_(ω1,ω) axiomatization for the class. We also characterize non-splitting and show it has the same properties as non-forking in superstable first order theories. Finally, we characterize equality, orthogonality and domination of (Galois) types in that MAEC.