On bounded \(m\)-reducibilities

Conditions for classes \({\mathfrak F}^1,{\mathfrak F}^0\) of non-decreasing total one-place arithmetic functions to define reducibility   \(\leq_m[^{{\mathfrak R}^1}_{{\mathfrak R}^0}]\leftrightharpoons\{(A,B)|A,B\subseteq\mathbb N\ \&\ (\exists \mbox{ r.f. }\ h) (\exists f_1\in{\mathfrak F...

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Datum:2018
1. Verfasser: Belyaev, Vladimir N.
Format: Artikel
Sprache:English
Veröffentlicht: Lugansk National Taras Shevchenko University 2018
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Online Zugang:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/932
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Назва журналу:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id admjournalluguniveduua-article-932
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spelling admjournalluguniveduua-article-9322018-03-21T06:34:59Z On bounded \(m\)-reducibilities Belyaev, Vladimir N. bounded reducibilities, degrees of unsolvability, singular reducibility, cylinder, indecomposable degree 03D20, 03D25, 03D30 Conditions for classes \({\mathfrak F}^1,{\mathfrak F}^0\) of non-decreasing total one-place arithmetic functions to define reducibility   \(\leq_m[^{{\mathfrak R}^1}_{{\mathfrak R}^0}]\leftrightharpoons\{(A,B)|A,B\subseteq\mathbb N\ \&\ (\exists \mbox{ r.f. }\ h) (\exists f_1\in{\mathfrak F}^1)(\exists f_0\in{\mathfrak F}^0) \) \([A\le_m^h\,B\ \&\ f_0\unlhd h\unlhd f_1]\}\) where \(k\unlhd l\) means that function \(l\) majors function \(k\) almost everywhere are studied. It is proved that the system of these reducibilities is highly ramified, and examples are constructed which differ drastically \(\leq_m[^{{\mathfrak R}^1}_{{\mathfrak R}^0}]\) from the standard m-reducibility  with respect to systems of degrees. Indecomposable and recursive degrees are considered. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/932 Algebra and Discrete Mathematics; Vol 4, No 2 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/932/461 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-21T06:34:59Z
collection OJS
language English
topic bounded reducibilities
degrees of unsolvability
singular reducibility
cylinder
indecomposable degree
03D20
03D25
03D30
spellingShingle bounded reducibilities
degrees of unsolvability
singular reducibility
cylinder
indecomposable degree
03D20
03D25
03D30
Belyaev, Vladimir N.
On bounded \(m\)-reducibilities
topic_facet bounded reducibilities
degrees of unsolvability
singular reducibility
cylinder
indecomposable degree
03D20
03D25
03D30
format Article
author Belyaev, Vladimir N.
author_facet Belyaev, Vladimir N.
author_sort Belyaev, Vladimir N.
title On bounded \(m\)-reducibilities
title_short On bounded \(m\)-reducibilities
title_full On bounded \(m\)-reducibilities
title_fullStr On bounded \(m\)-reducibilities
title_full_unstemmed On bounded \(m\)-reducibilities
title_sort on bounded \(m\)-reducibilities
description Conditions for classes \({\mathfrak F}^1,{\mathfrak F}^0\) of non-decreasing total one-place arithmetic functions to define reducibility   \(\leq_m[^{{\mathfrak R}^1}_{{\mathfrak R}^0}]\leftrightharpoons\{(A,B)|A,B\subseteq\mathbb N\ \&\ (\exists \mbox{ r.f. }\ h) (\exists f_1\in{\mathfrak F}^1)(\exists f_0\in{\mathfrak F}^0) \) \([A\le_m^h\,B\ \&\ f_0\unlhd h\unlhd f_1]\}\) where \(k\unlhd l\) means that function \(l\) majors function \(k\) almost everywhere are studied. It is proved that the system of these reducibilities is highly ramified, and examples are constructed which differ drastically \(\leq_m[^{{\mathfrak R}^1}_{{\mathfrak R}^0}]\) from the standard m-reducibility  with respect to systems of degrees. Indecomposable and recursive degrees are considered.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/932
work_keys_str_mv AT belyaevvladimirn onboundedmreducibilities
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