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2083-02.pdf | 1.61 MB | Adobe PDF | 見る/開く |
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dc.contributor.author | Mizusawa, Yuki | en |
dc.contributor.author | Ban, Koichiro | en |
dc.contributor.author | Suzuki, Toshio | en |
dc.contributor.alternative | 水澤, 勇気 | ja |
dc.contributor.alternative | 伴, 滉一郎 | ja |
dc.contributor.alternative | 鈴木, 登志雄 | ja |
dc.contributor.transcription | ミズサワ, ユウキ | - |
dc.contributor.transcription | バン, コウイチロウ | - |
dc.contributor.transcription | スズキ, トシオ | - |
dc.date.accessioned | 2019-06-24T02:55:20Z | - |
dc.date.available | 2019-06-24T02:55:20Z | - |
dc.date.issued | 2018-08 | - |
dc.identifier.issn | 1880-2818 | - |
dc.identifier.uri | http://hdl.handle.net/2433/242192 | - |
dc.description.abstract | Wu (2006) showed that every nonzero computably enumerable degree splits into two 1-generic degrees, and therefore, no two computably enumerable degrees bound the same class of 1-generic degrees. By relativizing this result with respect to the Lachlan set, it can be shown that (*) every nonzero d.c.e. degree splits into four 1-generic degrees. Here, a set A is d.c.e. (or, 2-c.e.) if there are two computably enumerable sets B and C such that A = B-C (set difference). Turing degree of a d.c.e. set is called a d.c.e. degree. By (*), no two d.c.e. degrees bound the same class of 1-generic degrees. Chong and Yu (2016) improved the result (*). In fact, it is split into two 1-generic degrees. In this note, we propose a construction with rollbacks of stages. By means of this construction, we give an alternative proof of (*). | en |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | 京都大学数理解析研究所 | ja |
dc.publisher.alternative | Research Institute for Mathematical Sciences, Kyoto University | en |
dc.subject | 1-generic set | en |
dc.subject | Ershov hierarchy | en |
dc.subject | d.c.e. set | en |
dc.subject | 2-c.e. set | en |
dc.subject.ndc | 410 | - |
dc.title | An Alternative Proof of 1-Generic Splittings (Proof theory and proving) | en |
dc.type | departmental bulletin paper | - |
dc.type.niitype | Departmental Bulletin Paper | - |
dc.identifier.ncid | AN00061013 | - |
dc.identifier.jtitle | 数理解析研究所講究録 | ja |
dc.identifier.volume | 2083 | - |
dc.identifier.spage | 8 | - |
dc.identifier.epage | 25 | - |
dc.textversion | publisher | - |
dc.sortkey | 02 | - |
dc.address | Dept. of Math. and Information Sci., Tokyo Metropolitan University | en |
dc.address | Dept. of Math. and Information Sci., Tokyo Metropolitan University | en |
dc.address | Dept. of Math. and Information Sci., Tokyo Metropolitan University | en |
dc.address.alternative | 首都大学東京 | ja |
dc.address.alternative | 首都大学東京 | ja |
dc.address.alternative | 首都大学東京 | ja |
dcterms.accessRights | open access | - |
datacite.awardNumber | 16K05255 | - |
dc.identifier.jtitle-alternative | RIMS Kokyuroku | en |
jpcoar.funderName | 日本学術振興会 | ja |
jpcoar.funderName.alternative | Japan Society for the Promotion of Science (JSPS) | en |
出現コレクション: | 2083 証明論と証明活動 |
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