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The additive group of the rationals does not have an automatic presentation
Journal of Symbolic Logic 76 (4):1341-1351 (2011)
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 ⊕ p∈I Z(p ∞ ), where I is an infinite set of primesOther Versions
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Citations of this work
Foundations of online structure theory.Nikolay Bazhenov, Rod Downey, Iskander Kalimullin & Alexander Melnikov - 2019 - Bulletin of Symbolic Logic 25 (2):141-181.
Computable Abelian groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
Online, computable and punctual structure theory.Matthew Askes & Rod Downey - 2023 - Logic Journal of the IGPL 31 (6):1251-1293.
Automatic models of first order theories.Pavel Semukhin & Frank Stephan - 2013 - Annals of Pure and Applied Logic 164 (9):837-854.
References found in this work
Finite automata presentable Abelian groups.André Nies & Pavel Semukhin - 2010 - Annals of Pure and Applied Logic 161 (3):458-467.
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