Omega-stability of a theory ($|S_1(A)|\le {\aleph }_0\text{for countable }A$)

A complete theory in a countable first-order language is omega-stable if over every countable set of parameters it has only countably many complete one-types. The theory of a free bijection is an example: a new point is either a specified integer translate of a parameter or lies in a new orbit. It is omega-stable but not omega-categorical.