Meager forking and \(m\)-independence (Q1126703)

Superstable theories \(T\) in a countable first-order language are considered. Vaught's conjecture for such theories says that if \(T\) has \(<2^{\aleph_0}\) countable models, then \(T\) has countably many of them. An important problem arising in the context of Vaught's conjecture is to describe the ways in which a type in \(T\) may be non-isolated (in the topological structure of the space of types), and to describe the sets of stationarizations of such a type. The author describes meager forking, \(m\)-independence and related notions intended for classifying countable models of \(T\).