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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 3, Pages 97–101 (Mi ivm9097)  
This article is cited in 1 scientific paper (total in 1 paper)

Brief communications

Limitwise monotonic reducibility on sets and on pairs of sets

D. Kh. Zainetdinov

Chair of Algebra and Mathematical Logic, Kazan (Volga Region) Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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Abstract: We study limitwise monotonic sets and pairs of sets. We investigate the properties of limitwise monotonic reducibility between sets and pairs of sets defined in terms of $\Sigma$-reducibility corresponding to initial segment of sets. In addition, we obtain a description of $\Sigma$-reducibility of families of a special form in terms of $lm$-reducibility. At the same time we show the relationship of concepts of $lm$-reducibility and $\Sigma$-reducibility between the pairs of sets.
Keywords: computable functions, $\Sigma$-reducibility, $\Sigma^0_2$-sets, limitwise monotonic function, limitwise monotonic sets, limitwise monotonic reducibility, pair of sets, family of subsets of natural numbers.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-31200
15-31-20607
Ministry of Education and Science of the Russian Federation 1.2045.2014
Presented by the member of Editorial Board: M. M. Arslanov
Received: 11.09.2015
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 3, Pages 85–88
DOI: https://doi.org/10.3103/S1066369X16030117
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: D. Kh. Zainetdinov, “Limitwise monotonic reducibility on sets and on pairs of sets”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 3, 97–101; Russian Math. (Iz. VUZ), 60:3 (2016), 85–88
Citation in format AMSBIB
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    • This publication is cited in the following 1 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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