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

Journal of Symbolic Logic 76 (4):1341-1351 (2011)
  Copy   BIBTEX

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 primes

Categories

Keywords

Reprint years

DOI

10.2178/jsl/1318338853

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 93,127

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Space complexity of Abelian groups.Douglas Cenzer, Rodney G. Downey, Jeffrey B. Remmel & Zia Uddin - 2009 - Archive for Mathematical Logic 48 (1):115-140.
Finite automata presentable Abelian groups.André Nies & Pavel Semukhin - 2010 - Annals of Pure and Applied Logic 161 (3):458-467.
The classification problem for p-local torsion-free Abelian groups of rank two.Greg Hjorth & Simon Thomas - 2006 - Journal of Mathematical Logic 6 (2):233-251.
On the complexity of the classification problem for torsion-free Abelian groups of finite rank.Simon Thomas - 2001 - Bulletin of Symbolic Logic 7 (3):329-344.
The dp-rank of Abelian groups.Yatir Halevi & Daniel Palacín - 2019 - Journal of Symbolic Logic 84 (3):957-986.
Borel reductions of profinite actions of SL n.Samuel Coskey - 2010 - Annals of Pure and Applied Logic 161 (10):1270-1279.
The additive groups of and with predicates for being square-free.Neer Bhardwaj & Chieu-Minh Tran - 2021 - Journal of Symbolic Logic 86 (4):1324-1349.
On Preservation of Stability for Finite Extensions of Abelian Groups.Frieder Haug - 1994 - Mathematical Logic Quarterly 40 (1):14-26.
Scott sentences for certain groups.Julia F. Knight & Vikram Saraph - 2018 - Archive for Mathematical Logic 57 (3-4):453-472.
On non-compact p-adic definable groups.Will Johnson & Ningyuan Yao - 2022 - Journal of Symbolic Logic 87 (1):188-213.

Analytics

Added to PP
2011-10-12

Downloads
10 (#1,222,590)

6 months
32 (#106,387)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Computable Abelian groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
Automatic models of first order theories.Pavel Semukhin & Frank Stephan - 2013 - Annals of Pure and Applied Logic 164 (9):837-854.
Online, computable and punctual structure theory.Matthew Askes & Rod Downey - 2023 - Logic Journal of the IGPL 31 (6):1251-1293.

Add more citations

References found in this work

Describing groups.André Nies - 2007 - Bulletin of Symbolic Logic 13 (3):305-339.
Finite automata presentable Abelian groups.André Nies & Pavel Semukhin - 2010 - Annals of Pure and Applied Logic 161 (3):458-467.

Add more references