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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*
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]

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2011

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