On the classification of simple inductive limit C*-algebras, II: The isomorphism theorem

In this article, it is proved that the invariant consisting of the scaled ordered K-group and the space of tracial states, together with the natural pairing between them, is a complete invariant for the class of unital simple C*-algebras which can be expressed as the inductive limit of a sequence A(1) -> A(2) -> ... -> A(n) -> ... with /A(n) = circle plus(tn)(i=1) Pn,iM[n,i](C(X-n,X-i))P-n,P-i, where X (n,i) is a compact metrizable space and P (n,i) is a projection in M-[n,M-i](C(X (n,i) )) for each n and i, and the spaces X-n,X-i are of uniformly bounded finite dimension. Note that the C*-algebras in the present class are not assumed to be of real rank zero, as they were in [EG2].