Topologies, Ranks, and Closures for Families of Theories. II

We describe topological properties, ranks, and closures as well as their dynamics for families of theories. Closures for families of theories are introduced based on sentences of the given theories. We look at properties of these closures and establish their relationship with standard closures. Values of e₁-spectra, as well as conditions for the existence of least generating sets, are characterized. Closures for linearly ordered families of theories are examined.