On the number of countable models of stable theories (Q2759151)

The aim of the paper is to prove that the number \(I(T,\aleph_0)\) of isomorphism classes of countable models of a countable, complete, stable, first-order theory having infinite models fulfills the condition \(I(T,\aleph_0)\geq \aleph_0\). In order to do so the author proves the fact that the condition above follows by the existence of a stationary, strongly nonisolated type over \(\emptyset\). Then the statement above is a consequence of the Lemma: Supposing that \(p\in S_1(\emptyset)\) is an accumulation point of types of definable elements one obtains that \(p\) is stationary and strongly nonisolated.