We prove that if T is a stable theory with only a finite number of countable models, then T contains a type-definable pseudoplane. We also show that for any stable theory T either T contains a type-definable pseudoplane or T is weakly normal.

We prove that every model of $T = \mathrm{Th}(\omega, countable) has an end extension; and that every countable theory with an infinite order and Skolem functions has 2 ℵ 0 nonisomorphic countable models; and that if every model of T has an end extension, then every |T|-universal model of T has an end extension definable with parameters.

Let T be a complete, countable, first-order theory with a finite number of countable models. Assuming that dcl(∅) is infinite we show that T has the strict order property.