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Punctual Copies of Algebraic Structures

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Abstract

We estimate the complexity of constructing a punctual “online” copy of an algebraic structure. We establish a general upper bound as well as optimal bounds for classes of Boolean algebras, abelian p-groups, and linear orders. Moreover, the methods developed here are applied to solving Montalbán’s open problem (2013) about copyable linear orders.

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Authors and Affiliations

  1. Kazan (Volga Region) Federal University, Kazan, Russia

    M. V. Zubkov, I. Sh. Kalimullin & A. N. Frolov

  2. Massey University, Albany, New Zealand

    A. G. Melnikov

Authors
  1. M. V. Zubkov
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  2. I. Sh. Kalimullin
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  3. A. G. Melnikov
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  4. A. N. Frolov
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Corresponding authors

Correspondence to M. V. Zubkov, I. Sh. Kalimullin, A. G. Melnikov or A. N. Frolov.

Additional information

Russian Text © The Author(s), 2019, published in Sibirskii Matematicheskii Zhurnal, 2019, Vol. 60, No. 6, pp. 1271–1285.

M. V. Zubkov was supported by the Russian Science Foundation (Grant 18—11—00028). I. Sh. Kalimullin was supported by the Ministry of Science and Education of the Russian Federation (Grant 1.451.2016/1.4). A. G. Melnikov was supported by the Marsden Fund of New Zealand. A. N. Frolov was supported by the President of the Russian Federation (Grant MD—2721.2019.1).

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Zubkov, M.V., Kalimullin, I.S., Melnikov, A.G. et al. Punctual Copies of Algebraic Structures. Sib Math J 60, 993–1002 (2019). https://doi.org/10.1134/S0037446619060077

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  • DOI: https://doi.org/10.1134/S0037446619060077

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