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Boolean universes above Boolean models

Published online by Cambridge University Press:  12 March 2014

Friedrich Wehrung
Friedrich Wehrung*
Affiliation:
Université de Caen, Departement de Mathématiques, 14032 Caen Cedex, France, E-mail: gremlin@amath.unicaen.fr
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Abstract

We establish several first- or second-order properties of models of first-order theories by considering their elements as atoms of a new universe of set theory and by extending naturally any structure of Boolean model on the atoms to the whole universe. For example, complete f-rings are “boundedly algebraically compact” in the language (+, −, ·, ∧, ∨, ≤), and the positive cone of a complete l-group with infinity adjoined is algebraically compact in the language (+, ∨, ≤). We also give an example with any first-order language. The proofs can be translated into “naive set theory” in a uniform way.

Keywords

AtomsBoolean modelsfirst-order languagesconvergence in lattice-ordered ringsequational compactnessalgebraic compactness

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 58 , Issue 4 , December 1993, pp. 1219 - 1250
Copyright
Copyright © Association for Symbolic Logic 1993

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