Structural properties of limitwise monotonic reducibility of sequences of sets
The paper is devoted to the study of limitwise monotonic sets, as well as to the investigation of the main structural properties of limitwise monotonic reducibility (lm-reducibility) between set and sequence of sets. Limitwise monotonic reducibility can be regarded as a special case of Σ-reducibilit...
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| Language: | English |
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Kazan Federal University
2018-09-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/structural-properties-of-limitwise-monotonic-403856.html |
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| _version_ | 1846145485772947456 |
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| author | D.Kh. Zainetdinov |
| author_facet | D.Kh. Zainetdinov |
| author_sort | D.Kh. Zainetdinov |
| collection | DOAJ |
| description | The paper is devoted to the study of limitwise monotonic sets, as well as to the investigation of the main structural properties of limitwise monotonic reducibility (lm-reducibility) between set and sequence of sets. Limitwise monotonic reducibility can be regarded as a special case of Σ-reducibility defined on families of initial segments of natural numbers. In this paper, lm-reducibility between set and sequence consisting of infinite sets has been considered in the language of the limitwise monotonic operator. The main result of this paper is the proof of the absence of the least non-limitwise monotonic sequence with respect to lm-reducibility between set and sequence of sets. This result as been proved with the help of the infinite injury priority method with the use of the tree of strategies. The result presented in this paper is a generalization of the result that there are no least non-limitwise monotonic Σ20-set under lm-reducibility of sets. |
| format | Article |
| id | doaj-art-c20bdd55764d48a789320052e66da5c6 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2018-09-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-c20bdd55764d48a789320052e66da5c62024-12-02T05:56:54ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982018-09-011603517527Structural properties of limitwise monotonic reducibility of sequences of setsD.Kh. Zainetdinov0Kazan Federal University, Kazan, 420008 RussiaThe paper is devoted to the study of limitwise monotonic sets, as well as to the investigation of the main structural properties of limitwise monotonic reducibility (lm-reducibility) between set and sequence of sets. Limitwise monotonic reducibility can be regarded as a special case of Σ-reducibility defined on families of initial segments of natural numbers. In this paper, lm-reducibility between set and sequence consisting of infinite sets has been considered in the language of the limitwise monotonic operator. The main result of this paper is the proof of the absence of the least non-limitwise monotonic sequence with respect to lm-reducibility between set and sequence of sets. This result as been proved with the help of the infinite injury priority method with the use of the tree of strategies. The result presented in this paper is a generalization of the result that there are no least non-limitwise monotonic Σ20-set under lm-reducibility of sets.https://kpfu.ru/structural-properties-of-limitwise-monotonic-403856.htmllimitwise monotonic functionlimitwise monotonic setlimitwise monotonic operatorlimitwise monotonic reducibilitysequence of setsσ20-set |
| spellingShingle | D.Kh. Zainetdinov Structural properties of limitwise monotonic reducibility of sequences of sets Учёные записки Казанского университета: Серия Физико-математические науки limitwise monotonic function limitwise monotonic set limitwise monotonic operator limitwise monotonic reducibility sequence of sets σ20-set |
| title | Structural properties of limitwise monotonic reducibility of sequences of sets |
| title_full | Structural properties of limitwise monotonic reducibility of sequences of sets |
| title_fullStr | Structural properties of limitwise monotonic reducibility of sequences of sets |
| title_full_unstemmed | Structural properties of limitwise monotonic reducibility of sequences of sets |
| title_short | Structural properties of limitwise monotonic reducibility of sequences of sets |
| title_sort | structural properties of limitwise monotonic reducibility of sequences of sets |
| topic | limitwise monotonic function limitwise monotonic set limitwise monotonic operator limitwise monotonic reducibility sequence of sets σ20-set |
| url | https://kpfu.ru/structural-properties-of-limitwise-monotonic-403856.html |
| work_keys_str_mv | AT dkhzainetdinov structuralpropertiesoflimitwisemonotonicreducibilityofsequencesofsets |