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.

We prove a dichotomy theorem for minimal structures and use it to prove that the number of non-isomorphic countable elementary extensions of an arbitrary countable, infinite first-order structure is infinite.

We construct a new class of 1 categorical structures, disproving Zilber's conjecture, and study some of their properties.

We construct a type p with preweight ω with respect to itself in a theory with few types. A type with this property must be present in a stable theory with finitely many (but more than one) countable models. The construction is a modification of Hrushovski's important pseudoplane construction.

We define a generalized notion of rank for stable theories without dense forking chains, and use it to derive that every type is domination-equivalent to a finite product of regular types. We apply this to show that in a small theory admitting finite coding, no realisation of a nonforking extension of some strong type can be algebraic over some realisation of a forking extension.

We show that the free pseudospace is a reduct of a 1-based theory. This answers a question of David M. Evans. The theory is superstable, but not ω-stable.