Classification of Certain Inductive Limit Type Actions on Approximate Interval Algebras

In this paper we present a classification, up to equivariant isomorphism, of C*-dynamical systems (A,ℝ, α) arising as inductive limits of directed systems {(A_n,ℝ, α_n ), φ_nm} where each A_n is a finite direct sum of matrix algebras over the continuous functions on the unit interval and the α_n is generated by an inner derivation coming from a self-adjoint element with finite spectrum.