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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| Дата: | 2018 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/932 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543277566656512 |
|---|---|
| author | Belyaev, Vladimir N. |
| author_facet | Belyaev, Vladimir N. |
| author_sort | Belyaev, Vladimir N. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-03-21T06:34:59Z |
| 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. |
| first_indexed | 2025-12-02T15:33:24Z |
| format | Article |
| id | admjournalluguniveduua-article-932 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:33:24Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| 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 |
| spellingShingle | bounded reducibilities degrees of unsolvability singular reducibility cylinder indecomposable degree 03D20 03D25 03D30 Belyaev, Vladimir N. On bounded \(m\)-reducibilities |
| title | On bounded \(m\)-reducibilities |
| title_full | On bounded \(m\)-reducibilities |
| title_fullStr | On bounded \(m\)-reducibilities |
| title_full_unstemmed | On bounded \(m\)-reducibilities |
| title_short | On bounded \(m\)-reducibilities |
| title_sort | on bounded \(m\)-reducibilities |
| topic | bounded reducibilities degrees of unsolvability singular reducibility cylinder indecomposable degree 03D20 03D25 03D30 |
| topic_facet | bounded reducibilities degrees of unsolvability singular reducibility cylinder indecomposable degree 03D20 03D25 03D30 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/932 |
| work_keys_str_mv | AT belyaevvladimirn onboundedmreducibilities |