Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint

Notre Dame Journal of Formal Logic 48 (3):399-423 (2007)
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
Keywords Rumely domains   model completeness   decidability
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