Jesse Mazer wrote
>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.