Filtral powers of structures

Journal of Symbolic Logic 63 (4):1239-1254 (1998)
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 K be an elementary class closed under updirected unions (e.g., if K is an amalgamation class); then K is closed under finite products if and only if K is closed under reduced products if and only if K is a Horn class
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