On Decidable Extensions of Presburger Arithmetic: From A. Bertrand Numeration Systems to Pisot Numbers
Point, Francoise
J. Symbolic Logic, Tome 65 (2000) no. 1, p. 1347-1374 / Harvested from Project Euclid
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We study extensions of Presburger arithmetic with a unary predicate R and we show that under certain conditions on R, R is sparse (a notion introduced by A. L. Semenov) and the theory of $\langle\mathbb{N}, +, R\rangle$ is decidable. We axiomatize this theory and we show that in a reasonable language, it admits quantifier elimination. We obtain similar results for the structure $\langle\mathbb{Q},+, R\rangle$.
Publié le : 2000-09-14
Classification:  
@article{1183746185,
     author = {Point, Francoise},
     title = {On Decidable Extensions of Presburger Arithmetic: From A. Bertrand Numeration Systems to Pisot Numbers},
     journal = {J. Symbolic Logic},
     volume = {65},
     number = {1},
     year = {2000},
     pages = { 1347-1374},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183746185}
}

Point, Francoise. On Decidable Extensions of Presburger Arithmetic: From A. Bertrand Numeration Systems to Pisot Numbers. J. Symbolic Logic, Tome 65 (2000) no. 1, pp.  1347-1374. http://gdmltest.u-ga.fr/item/1183746185/