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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 158, Pages 81–115
(Mi into413)
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This article is cited in 3 scientific papers (total in 3 papers)
Computable presentability of countable linear orders
A. N. Frolov Kazan (Volga Region) Federal University
Abstract:
The main goal of this paper is to study algorithmic properties of countable linear orders by constructing effective presentations of these structures on the set of natural numbers. In 1991, C. Jockusch and R. Soare constructed a low linear order without computable presentations. Before in 1989, R. Downey and M. Moses showed that each low discrete linear order has a computable copy. It is natural to ask for which order types of low presentations it is sufficient the existence of a computable presentation. This question (namely, research program) was stated by R. Downey in 1998: Describe the order property $P$ such that, for any low linear order $L$, $P(L)$ implies the existence of a computable presentation of $L$. In this paper, we give a detailed review of the main results in this direction. These results are mostly obtained by the author or in co-authorship.
Keywords:
countable linear orders, computable structures, computable presentability, low degrees.
Citation:
A. N. Frolov, “Computable presentability of countable linear orders”, Proceedings of the Seminar on Algebra and Mathematical Logic of the Kazan (Volga Region) Federal University, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 158, VINITI, Moscow, 2018, 81–115; J. Math. Sci. (N. Y.), 256:2 (2021), 199–233
Linking options:
https://www.mathnet.ru/eng/into413 https://www.mathnet.ru/eng/into/v158/p81
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Abstract page: | 126 | Full-text PDF : | 39 | References: | 8 |
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