Forking and stability in the representations of a C*-algebra

TL;DR

This paper proves that the theory of non-degenerate C*-algebra representations is superstable, characterizes forking and related concepts, and demonstrates weak elimination of imaginaries, advancing the understanding of their model-theoretic properties.

Contribution

It establishes the superstability of the theory of non-degenerate C*-algebra representations and characterizes key model-theoretic notions within this framework.

Findings

The theory of non-degenerate representations is superstable.

Forking, orthogonality, and domination are characterized.

The theory exhibits weak elimination of imaginaries.

Abstract

We show that the theory of a non-degenerate representation of a C*-algebra A over a Hilbert space H is superstable. Also, we characterize forking, orthogonality and domination of types and show that the theory has weak elimination of imaginaries.