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On decidable extensions of Presburger arithmetic: from A. Bertrand numeration sytems to Pisot numbers

Published online by Cambridge University Press:  12 March 2014

Françoise Point
Françoise Point*
Affiliation:
Senior Research Associate F.N.R.S., Université Mons-Hainaut, 6, Avenue du Champ de Mars, 7, 000 Mons, Belgium E-mail: point@lpgique.jussieu.fr
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Abstract

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. Semënov) and the theory of 〈ℕ, +, R〉 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 〈ℚ, +, R〉.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 3 , September 2000 , pp. 1347 - 1374
Copyright
Copyright © Association for Symbolic Logic 2000

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