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.
Publié le : 2007-07-14
Classification:
Rumely domains,
model completeness,
decidability,
03C10,
11U99
@article{1187031411,
author = {Sureson, Claude},
title = {Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint},
journal = {Notre Dame J. Formal Logic},
volume = {48},
number = {1},
year = {2007},
pages = { 399-423},
language = {en},
url = {http://dml.mathdoc.fr/item/1187031411}
}
Sureson, Claude. Rumely Domains with Atomic Constructible Boolean Algebra. An Effective Viewpoint. Notre Dame J. Formal Logic, Tome 48 (2007) no. 1, pp. 399-423. http://gdmltest.u-ga.fr/item/1187031411/