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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A structure of punctual dimension two
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by Alexander Melnikov and Keng Meng Ng PDF
Proc. Amer. Math. Soc. 148 (2020), 3113-3128 Request permission

Abstract:

This paper contributes to the general program which aims to eliminate an unbounded search from proofs and procedures in computable structure theory. A countable structure in a finite language is punctual if its domain is $\omega$ and its operations and relations are primitive recursive. A function $f$ is punctual if both $f$ and $f^{-1}$ are primitive recursive. We prove that there exists a countable rigid algebraic structure which has exactly two punctual presentations, up to punctual isomorphism.
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Additional Information
  • Alexander Melnikov
  • Affiliation: Department of Mathematics, Massey University Auckland, Private Bag 102904, North Shore, Auckland 0745, New Zealand
  • Email: alexander.g.melnikov@gmail.com
  • Keng Meng Ng
  • Affiliation: Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
  • MR Author ID: 833062
  • Email: selwyn.km.ng@gmail.com
  • Received by editor(s): October 6, 2019
  • Published electronically: April 14, 2020
  • Additional Notes: The first author was partially supported by the Marsden Foundation of New Zealand.
    The second author was partially supported by the grants MOE2015-T2-2-055 and RG131/17.
  • Communicated by: Heike Mildenberger
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 3113-3128
  • MSC (2010): Primary 03D45; Secondary 03D20, 03D15
  • DOI: https://doi.org/10.1090/proc/15020
  • MathSciNet review: 4099797