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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 10, Pages 3–14
DOI: https://doi.org/10.26907/0021-3446-2021-10-3-14 (Mi ivm9717) 		 
Asymptotic density and computability

I. I. Batyrshin

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
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DOI: https://doi.org/10.26907/0021-3446-2021-10-3-14
Abstract: We show that a set is bi-immune if and only if there are no computable permutations that arrange the set into a generically computable set or an effectively densely computable set. An example of a coarsely computable bi-immune set is constructed. It is also proved that for any set there is a permutation from the same Turing degree that arranges the set into an effectively densely computable set. The upper densities of some sets are studied.
Keywords: asymptotic density, generic complexity, bi-immune set, Turing degree.
Funding agency Grant number
Russian Science Foundation 18-11-00028
Received: 02.11.2020
Revised: 02.11.2020
Accepted: 30.03.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 10, Pages 1–9
DOI: https://doi.org/10.3103/S1066369X21100017
Document Type: Article
UDC: 510.5
Language: Russian
Citation: I. I. Batyrshin, “Asymptotic density and computability”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 10, 3–14; Russian Math. (Iz. VUZ), 65:10 (2021), 1–9
Citation in format AMSBIB
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\by I.~I.~Batyrshin
\paper Asymptotic density and computability
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 10
\pages 3--14
\mathnet{http://mi.mathnet.ru/ivm9717}
\crossref{https://doi.org/10.26907/0021-3446-2021-10-3-14}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2021
\vol 65
\issue 10
\pages 1--9
\crossref{https://doi.org/10.3103/S1066369X21100017}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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