Instability and Theories with Few Models
A. Pillay · Proceedings of the American Mathematical Society · 1980
Some results are obtained concerning $n(T)$, the number of countable models up to isomorphism, of a countable complete first order theory T. It is first proved that if $n(T) = 3$ and T has a tight prime model, then T is unstable. Secondly, it is proved that if $n(T)$ is finite and more than one, and T has few links, then T is unstable. Lastly we show that if T has an algebraic model and has few links, then $n(T)$ is infinite.