Some Boolean algebras with finitely many distinguished ideals II
✍ Scribed by Regina Aragón
- Publisher
- John Wiley and Sons
- Year
- 2003
- Tongue
- English
- Weight
- 291 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0044-3050
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✦ Synopsis
Abstract
We describe the countably saturated models and prime models (up to isomorphism) of the theory Th~prin~ of Boolean algebras with a principal ideal, the theory Th~max~ of Boolean algebras with a maximal ideal, the theory Th~ac~ of atomic Boolean algebras with an ideal such that the supremum of the ideal exists, and the theory Th~sa~ of atomless Boolean algebras with an ideal such that the supremum of the ideal exists. We prove that there are infinitely many completions of the theory of Boolean algebras with a distinguished ideal that do not have a countably saturated model. Also, we give a sufficient condition for a model of the theory T~X~ of Boolean algebras with distinguished ideals to be elementarily equivalent to a countably saturated model of T~X~.