  We show that the common theory of all modules over a tubular algebra (over a
recursive algebraically closed field) is decidable. This result supports a long
standing conjecture of Mike Prest which says that a finite-dimensional algebra
(over a recursively given field) is tame if and only its common theory of
modules is decidable. Moreover, as a corollary, we are able to confirm this
conjecture for the class of concealed canonical algebras over algebraically
closed fields. These are the first examples of non-domestic algebras which have
been shown to have decidable theory of modules.
