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Model theory of a Hilbert space expanded with an unbounded closed selfadjoint operator
Authors:Camilo Enrique Argoty Pulido
Institution:Departamento de Matemáticas, Universidad Sergio Arboleda, , Bogotá, Colombia
Abstract: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 suitable MAEC for such a structure, prove it is ?0‐categorical and ?0‐stable up to a system of perturbations. We give an explicit continuous urn:x-wiley:09425616:media:malq201110043:malq201110043-math-0001 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.
Keywords:
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