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Filtral powers of structures

Published online by Cambridge University Press:  12 March 2014

P. Ouwehand  and
H. Rose
P. Ouwehand
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7700, South Africa. E-mail: peter2@maths.uct.ac.za
H. Rose
Affiliation:
Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7700, South Africa. E-mail: rose@maths.uct.ac.za
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 63 , Issue 4 , December 1998 , pp. 1239 - 1254
Copyright
Copyright © Association for Symbolic Logic 1998

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References

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