Characterizing an א_ε-saturated model of superstable NDOP theories by its double-struck L sign _{∞, אε}- theory

Assume a complete countable first order theory is superstable with NDOP. We know that any א_ε-saturated model of the theory is א_ε-prime over a non-forking tree of "small" models and its isomorphism type can be characterized by its double-struck L sign_{∞, κ} (dimension qualifiers)-theory, or, if you prefer, appropriate cardinal invariants. We go one step further by providing cardinal invariants which are as finitary as seem reasonable.