Inductive Limits of Inner Actions on Approximate Interval Algebras Generated by Elements With Finite Spectrum

In this paper we present a classification for C*-dynamical systems (A,ℝ,α) of the following form. There exists a sequence {A_n} of C*-algebras each isomorphic to a finite direct sum of matrix algebras over the unit interval, actions α_n of ℝ on A_n generated by elements with finite spectrum, and equivariant connecting ∗-homomorphisms φ_nm:A_n→A_m satisfying a certain technical assumption, such that (A,ℝ, α) is the limit of the inductive system {(A_n, α_n), φ_nm}.