The Journal of Symbolic Logic

Research Article

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

Todor Tsankov 

Analyse Fonctionnelle, Boîte 186, Université Paris 6, 4 Place Jussieu, 75252 Paris Cedex 05, France,

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 ⊕ pϵI Z(p ), where I is an infinite set of primes.

(Received May 24 2010)

Key words and phrases

  • automatic structures;
  • FA-presentable;
  • abelian groups;
  • additive combinatorics

Correspondence

Equipe de Logique, UFR de Mathématiques, Université Paris Diderot, 75205 Paris, CEDEX 13, France, E-mail: todor@math.jussieu.fr