ABSTRACT
In this chapter the material of the text is to culminate in Vaught's theorem saying that a countable complete theory cannot have, up to isomorphism, exactly two countable models (Theorem 13.4.1). This is a curious anomaly,1 for all other finite numbers do occur, as will be seen in §13.4. In itself the result is a good deal less consequential than its proof, which really uses almost everything we have done so far (and requires yet some more preparation). Thus we reach a certain highlight in this chapter in view of which it could well serve as the final topic of a one semester course. (The remaining two chapters, especially the last one, have a rather separate character.)
