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.
Citation
Claude Sureson. "Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint." Notre Dame J. Formal Logic 48 (3) 399 - 423, 2007. https://doi.org/10.1305/ndjfl/1187031411
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