Jesse Mazer wrote > [snip] > ... >Doesn't the UDA argument in some sense depend on the >idea of computing "in the limit" too?

Yes. This follows from the "invariance lemma", i.e. from the fact that the first persons cannot be aware of delays of "reconstitution" in UD* (the complete work of the UD). The domain of uncertainty can be defined by the collection of all maximal consistent extensions of our actual state/history. Those maximal extensions are not r.e. (not recursively enumerable, not algorithmically generable, not computable in some sense), but are r.e. in the limit, on which our average experiences will proceed (and this is enough for the working of the UDA). (An interesting paper from recursion theory which is relevant for *further* studies is the technical but readable paper by Posner 1980. Readable by beginners in Recursion Theory I mean. POSNER D.B. 1980, A Survey of non r.e. degrees ? O', in F.R. Drake and S.S. Wainer (eds), Recursion Theory: its generalisation and applications, Cambridge University Press.) I think that Schmidhuber has *different* motivations for the limit computable functions. There are also important in the field of inductive inference theory. Bruno