Notre Dame Journal of Formal Logic

Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint

Claude Sureson

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.

Article information

Source
Notre Dame J. Formal Logic Volume 48, Number 3 (2007), 399-423.

Dates
First available in Project Euclid: 13 August 2007

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

Subjects
Primary: 03C10: Quantifier elimination, model completeness and related topics
Secondary: 11U99: None of the above, but in this section

Keywords
Rumely domains model completeness decidability

Citation

Sureson, Claude. Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint. Notre Dame Journal of Formal Logic 48 (2007), no. 3, 399--423. doi:10.1305/ndjfl/1187031411. http://projecteuclid.org/euclid.ndjfl/1187031411.


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