## Journal of Symbolic Logic

### Filtral Powers of Structures

#### 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 $\omega$-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.

#### Article information

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

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745630

Mathematical Reviews number (MathSciNet)
MR1665710

Zentralblatt MATH identifier
0929.03040

JSTOR