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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Computable completely decomposable groups
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by Rodney Downey and Alexander G. Melnikov PDF
Trans. Amer. Math. Soc. 366 (2014), 4243-4266 Request permission

Abstract:

A completely decomposable group is an abelian group of the form $\bigoplus _i H_i$, where $H_i \leq (Q,+)$. We show that every computable completely decomposable group is $\Delta ^0_5$-categorical. We construct a computable completely decomposable group which is not $\Delta ^0_4$-categorical, and give an example of a computable completely decomposable group $G$ which is $\Delta ^0_4$-categorical but not $\Delta ^0_3$-categorical. We also prove that the index set of computable completely decomposable groups is arithmetical.
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Additional Information
  • Rodney Downey
  • Affiliation: School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, P. O. Box 600, Wellington, New Zealand
  • MR Author ID: 59535
  • Alexander G. Melnikov
  • Affiliation: Department of Mathematics, Nanyang Technological University, Singapore 639798 Singapore
  • MR Author ID: 878230
  • ORCID: 0000-0001-8781-7432
  • Received by editor(s): August 28, 2012
  • Published electronically: April 14, 2014
  • Additional Notes: We are thankful to Isaac Newton Institute for Mathematical Sciences and, more specifically, Semantics and Syntax: A Legacy of Alan Turing program, for partial support of our project. The first author thanks the Marsden Fund of New Zealand for its support. The second author’s research was also partially supported by SPMS, Nanyang Technological University, Singapore, and the University of Auckland, New Zealand. Many thanks to André Nies, Asher Kach and Kyle Riggs for pointing out numerous typos and minor mathematical problems in the early draft of the paper.
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 366 (2014), 4243-4266
  • MSC (2010): Primary 03D45, 03C57
  • DOI: https://doi.org/10.1090/S0002-9947-2014-06115-1
  • MathSciNet review: 3206458