Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint
Claude Sureson
Source: Notre Dame J. Formal Logic Volume 48, Number 3
(2007), 399-423.
Abstract
The archetypal Rumely domain is the ring \widetildeZ of algebraic integers. Its constructible Boolean algebra is atomless. We study here the opposite situation: Rumely domains whose constructible Boolean algebra is atomic. Recursive models (which are rings of algebraic numbers) are proposed; effective model-completeness and decidability of the corresponding theory are proved.
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Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1187031411
Digital Object Identifier: doi:10.1305/ndjfl/1187031411
Mathematical Reviews number (MathSciNet): MR2336355
Zentralblatt MATH identifier: 1158.03020
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