Σ -Reducibility and lm -Reducibility of Sets and Sequences of Sets
Limitwise monotonic sets, pairs of sets, and sequences consisting of infinite sets are studied in the paper. The main properties of limitwise monotonic reducibility between two sets, as well as between the set and a pair of sets defined in terms of Σ -reducibility of the corresponding families of a...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2016-03-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | http://kpfu.ru/portal/docs/F2144567341/158_1_phys_mat_4.pdf |
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| _version_ | 1849220867948544000 |
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| author | D.Kh. Zainetdinov |
| author_facet | D.Kh. Zainetdinov |
| author_sort | D.Kh. Zainetdinov |
| collection | DOAJ |
| description | Limitwise monotonic sets, pairs of sets, and sequences consisting of infinite sets are studied in the paper. The main properties of limitwise monotonic reducibility between two sets, as well as between the set and a pair of sets defined in terms of Σ -reducibility of the corresponding families of a special form, are considered. In addition, description of Σ -reducibility of the families of a special form in terms of lm-reducibility is obtained. The relationship between the concepts of lm -reducibility of the sequences of sets and Σ -reducibility of the families of a special form for the sequences of sets is demonstrated. |
| format | Article |
| id | doaj-art-d4422f081cad4bbea493e9b23d893b94 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2016-03-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-d4422f081cad4bbea493e9b23d893b942024-12-02T08:51:25ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982016-03-0115815165Σ -Reducibility and lm -Reducibility of Sets and Sequences of SetsD.Kh. Zainetdinov0Kazan Federal University, Kazan, 420008 RussiaLimitwise monotonic sets, pairs of sets, and sequences consisting of infinite sets are studied in the paper. The main properties of limitwise monotonic reducibility between two sets, as well as between the set and a pair of sets defined in terms of Σ -reducibility of the corresponding families of a special form, are considered. In addition, description of Σ -reducibility of the families of a special form in terms of lm-reducibility is obtained. The relationship between the concepts of lm -reducibility of the sequences of sets and Σ -reducibility of the families of a special form for the sequences of sets is demonstrated.http://kpfu.ru/portal/docs/F2144567341/158_1_phys_mat_4.pdfcomputable functionΣ -reducibilitylimitwise monotonic functionlimitwise monotonic setslimitwise monotonic reducibilitysequence of infinite setsfamily of subsets of natural numbers |
| spellingShingle | D.Kh. Zainetdinov Σ -Reducibility and lm -Reducibility of Sets and Sequences of Sets Учёные записки Казанского университета: Серия Физико-математические науки computable function Σ -reducibility limitwise monotonic function limitwise monotonic sets limitwise monotonic reducibility sequence of infinite sets family of subsets of natural numbers |
| title | Σ -Reducibility and lm -Reducibility of Sets and Sequences of Sets |
| title_full | Σ -Reducibility and lm -Reducibility of Sets and Sequences of Sets |
| title_fullStr | Σ -Reducibility and lm -Reducibility of Sets and Sequences of Sets |
| title_full_unstemmed | Σ -Reducibility and lm -Reducibility of Sets and Sequences of Sets |
| title_short | Σ -Reducibility and lm -Reducibility of Sets and Sequences of Sets |
| title_sort | σ reducibility and lm reducibility of sets and sequences of sets |
| topic | computable function Σ -reducibility limitwise monotonic function limitwise monotonic sets limitwise monotonic reducibility sequence of infinite sets family of subsets of natural numbers |
| url | http://kpfu.ru/portal/docs/F2144567341/158_1_phys_mat_4.pdf |
| work_keys_str_mv | AT dkhzainetdinov sreducibilityandlmreducibilityofsetsandsequencesofsets |