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A structure of punctual dimension two


Authors: Alexander Melnikov and Keng Meng Ng
Journal: Proc. Amer. Math. Soc. 148 (2020), 3113-3128
MSC (2010): Primary 03D45; Secondary 03D20, 03D15
DOI: https://doi.org/10.1090/proc/15020
Published electronically: April 14, 2020
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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
Email: selwyn.km.ng@gmail.com

DOI: https://doi.org/10.1090/proc/15020
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
Article copyright: © Copyright 2020 American Mathematical Society