Fix an infinite cardinal λ. The theory T is λ-stable
if for any model M of T of cardinality
at most λ there are no more than λ many one-types over
M. T is stable (without qualification) if it is λ-stable for some infinite λ. Stability is a robust condition being equivalent to the non-existence of a formula with the order property relative to T or to the finiteness of the local ranks (analogous to Morley rank) or to the presence of a good notion of forking or dependence. A countable theory is totally transcendental if and only if is ℵ0-stable. |