Filtral powers of structures
P. Ouwehand, H. Rose · Journal of Symbolic Logic · 1998
Abstract Among the results of this paper are the following: 1. Every Boolean (ultra)power is the union of an updirected elementary family of direct ultrapowers. 2. Under certain conditions, a finitely iterated Boolean ultrapower is isomorphic to a single Boolean ultrapower. 3. A ω-bounded filtral power is an elementary substructure of a filtral power. 4. Let be an elementary class closed under updirected unions (e.g., if is an amalgamation class); then is closed under finite products if and only if is closed under reduced products if and only if is a Horn class.