Countable models and unions of theories (Q1821096)

This paper is a natural continuation of the authors' paper reviewed above [see Zbl 0616.03019] in which we gave a partial positive solution to the following conjecture: There is no (first order) stable theory which has only n \((>1)\) countable models. More precisely, we showed that we cannot construct a theory with n \((>1)\) countable models by imitating the construction of Ehrenfeucht's example. In the present paper, we prove the above conjecture for those theories which can be conceived as limits of certain theories.