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Proceedings of the American Mathematical Society

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$\mathbb {Q}$ muni de l'arithmétique faible
de Penzin est décidable


Author: Françoise Delon
Journal: Proc. Amer. Math. Soc. 125 (1997), 2711-2717
MSC (1991): Primary 03C60; Secondary 12L05
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Abstract | References | Similar Articles | Additional Information

Abstract: We prove the decidability of the additive ordered group $\mathbb {Q}$ equipped with a predicate for $2^{\mathbb {Z}}$, the multiplication restricted to $2^{\mathbb {Z}}\times \mathbb {Q}$ and the $2$-adic valuation ranging in $2^{\mathbb {Z}}$.


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Additional Information

Françoise Delon
Affiliation: CNRS-Université Paris 7, UFR de Mathématiques, 2 place Jussieu, 75251 Paris cedex 05, France
Email: delon@logique.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03912-9
Keywords: Penzin arithmetic, decidability, field of rational numbers, $p$-adic valuation
Received by editor(s): September 20, 1995
Received by editor(s) in revised form: April 4, 1996
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society