TITLE: Are wild problems related to undecidable ones?
QUESTION [14 upvotes]: In representation theory, there is a well-known notion of a wild classification problem (such problems have been discussed often on this forum, for example, here). In logic, there is a notion of an undecidable problem.

Is there a theorem which says that there is something undecidable about a wild classification problem?

A reference where such issues are discussed would be very helpful.

REPLY [16 votes]: Yes, there is a connection, but I think it is conjectural in its full generality. The mosst general reference could be, where it is proven, that for a subclass of wild algebras, the representation theory is undecidable:
Mike Prest: Wild representation type and undecidability, Comm. Alg. 19 (3), 1991.
It is also well-known (it is stated with references for example in Benson), that the representation theory of the algebra used to define wildness (i.e. $k\langle X,Y\rangle$) is undecidable.