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

  • Todor Tsankov (a1)
  • DOI:
  • Published online: 01 March 2014

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.

Corresponding author
Equipe de Logique, UFR de Mathématiques, Université Paris Diderot, 75205 Paris, CEDEX 13, France, E-mail:
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
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