Remarks on Villadsen algebras, II: A generalized construction and the comparison radius function

The authors’ recent classification of Jesper Villadsen’s remarkable generalization (based on a self-reproducing seed space) of Glimm’s infinite tensor product (UHF) C*-algebras, by means of the Cuntz semigroup (in the case of a fixed, well-behaved, seed space), is extended to the analogous generalization of Bratteli’s approximately finite-dimensional (AF) C*-algebras. Some progress is made in the direction of distinguishing between algebras based on different seed spaces.