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The additive group of the rationals does not have an automatic presentation

Published online by Cambridge University Press:  12 March 2014

Todor Tsankov
Todor Tsankov*
Affiliation:
Analyse Fonctionnelle, Boîte 186, Université Paris6, 4 Place Jussieu, 75252 Paris Cedex 05, France,
*
Equipe de Logique, UFR de Mathématiques, Université Paris Diderot, 75205 Paris, CEDEX 13, France, E-mail: [email protected]
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Abstract

We prove that the additive group of the rationals does not have an automatic presentation. The proof also applies to certain other abelian groups, for example, torsion-free groups that are p-divisible for infinitely many primes p, or groups of the form ⊕pϵIZ(p∞), where I is an infinite set of primes.

Keywords

automatic structuresFA-presentableabelian groupsadditive combinatorics
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1341 - 1351
Copyright
Copyright © Association for Symbolic Logic 2011

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