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Undecidable extensions of Büchi arithmetic and Cobham-Semënov Theorem

Published online by Cambridge University Press:  12 March 2014

Alexis Bès
Alexis Bès*
Affiliation:
Equipe de Logique, Université Paris7, 2, Place Jussieu, 75251 Paris Cedex 05, France E-mail: bes@logique.jussieu.fr
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Abstract

Let k and l be two multiplicatively independent integers, and let L ⊆ ℕn be a l-recognizable set which is not definable in 〈ℕ; +〉. We prove that the elementary theory of 〈ℕ; +, Vk, L〉, where Vk(x) denotes the greatest power of k dividing x, is undecidable. This result leads to a new proof of the Cobham-Semënov theorem.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 62 , Issue 4 , December 1997 , pp. 1280 - 1296
Copyright
Copyright © Association for Symbolic Logic 1997

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References

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