ON  COMPUTABLE MODELS OF THEORIES

                  Bakhadyr Khoussainov

Let T be a consistent theory of the first order predicate
calculus. The following two questions arise naturally when one
is interested in computable models of T:

1. Which models of T possess computable presentations?
   In particular, does T have a computable model?
2. How do computable models of T interact with each other?
   In particular, does T have a computable model with exactly n,
   where n > 0, computable isomorphism types?

We discuss these and related questions for omega-categorical
theories, omega_1-categorical theories, and for Ehrenfeucht theories.