Journal of Symbolic Logic

Filtral Powers of Structures

P. Ouwehand and H. Rose

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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 $\omega$-bounded filtral power is an elementary substructure of a filtral power. 4. Let $\mathscr{K}$ be an elementary class closed under updirected unions (e.g., if $\mathscr{K}$ is an amalgamation class); then $\mathscr{K}$ is closed under finite products if and only if $\mathscr{K}$ is closed under reduced products if and only if $\mathscr{K}$ is a Horn class.

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J. Symbolic Logic, Volume 63, Issue 4 (1998), 1239-1254.

First available in Project Euclid: 6 July 2007

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Ouwehand, P.; Rose, H. Filtral Powers of Structures. J. Symbolic Logic 63 (1998), no. 4, 1239--1254.

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