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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 6, Pages 15–26 (Mi ivm9119)  

This article is cited in 4 scientific papers (total in 4 papers)

Initial segments of computable linear orders with computable natural relations

R. I. Bikmukhametov

Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
Full-text PDF (229 kB) Citations (4)
References:
Abstract: We study the algorithmic complexity of natural relations on initial segments of computable linear orders. We prove that there exists a computable linear order with computable density relation such that its $\Pi^0_1$-initial segment has no computable presentation with computable density relation. We also prove that the same holds for right limit and left limit relations.
Keywords: linear orders, initial segments, density relation, right limit relation, left limit relation.
Funding agency Grant number
Russian Foundation for Basic Research 15-41-02507
15-31-20607
15-01-08252
Ministry of Education and Science of the Russian Federation 1.2045.2014
Received: 17.10.2014
Revised: 19.01.2015
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 6, Pages 12–20
DOI: https://doi.org/10.3103/S1066369X16060025
Bibliographic databases:
Document Type: Article
UDC: 510.532
Language: Russian
Citation: R. I. Bikmukhametov, “Initial segments of computable linear orders with computable natural relations”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 6, 15–26; Russian Math. (Iz. VUZ), 60:6 (2016), 12–20
Citation in format AMSBIB
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\pages 15--26
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\vol 60
\issue 6
\pages 12--20
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  • https://www.mathnet.ru/eng/ivm/y2016/i6/p15
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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