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Rational sequences converging to left-c.e. reals of positive effective Hausdorff dimension
http://hdl.handle.net/10748/0002000800
http://hdl.handle.net/10748/00020008002a4f345e-a0d5-4434-871a-23151d8ed5d5
| 名前 / ファイル | ライセンス | アクション |
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11170-001.pdf (137.3 KB)
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| Item type | デフォルトアイテムタイプ（フル）(1) | |||||||||||||||
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| 公開日 | 2024-10-21 | |||||||||||||||
| タイトル | ||||||||||||||||
| タイトル | Rational sequences converging to left-c.e. reals of positive effective Hausdorff dimension | |||||||||||||||
| 言語 | en | |||||||||||||||
| 作成者 |
IMAI, Hiroyuki
× IMAI, Hiroyuki
× KUMABE, Masahiro
× MIYABE, Kenshi
× MIZUSAWA, Yuki
× SUZUKI, Toshio
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| 寄与者 | ||||||||||||||||
| 寄与者タイプ | Editor | |||||||||||||||
| 姓名 | PENG, N | |||||||||||||||
| 言語 | en | |||||||||||||||
| 寄与者 | ||||||||||||||||
| 寄与者タイプ | Editor | |||||||||||||||
| 姓名 | TANAKA, K | |||||||||||||||
| 言語 | en | |||||||||||||||
| 寄与者 | ||||||||||||||||
| 寄与者タイプ | Editor | |||||||||||||||
| 姓名 | YANG, Y | |||||||||||||||
| 言語 | en | |||||||||||||||
| 寄与者 | ||||||||||||||||
| 寄与者タイプ | Editor | |||||||||||||||
| 姓名 | WU, G | |||||||||||||||
| 言語 | en | |||||||||||||||
| 寄与者 | ||||||||||||||||
| 寄与者タイプ | Editor | |||||||||||||||
| 姓名 | YU, L | |||||||||||||||
| 言語 | en | |||||||||||||||
| 内容記述 | ||||||||||||||||
| 内容記述タイプ | Abstract | |||||||||||||||
| 内容記述 | In our previous work, we characterized Solovay reducibility using Lipschitz condition, and introduced quasi Solovay reducibility (qS-reducibility, for short) as a H¨older condition counterpart. In this paper, we investigate effective dimensions and ideals closely related to quasi Solovay reducibility by means of the rate of convergence. We show that the qS-completeness among left-c.e. reals is equivalent to having a positive effective Hausdorff dimension. The Solovay degrees of qS-complete left-c.e. reals form a filter. On the other hand, the Solovay degrees of non-qS-complete left-c.e. reals do not form an ideal. Based on observations on the relationships between rational sequences and reducibility, we introduce a stronger version of qS-reducibility. Given a degree of this reducibility, the lower cone (including the given degree) forms an ideal. By developing these investigations, we characterize the effective dimensions by means of the rate of convergence. We give a variation of the first incompleteness theorem based on Solovay reducibility. |
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| 言語 | en | |||||||||||||||
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| 言語 | eng | |||||||||||||||
| 資源タイプ | ||||||||||||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_5794 | |||||||||||||||
| 資源タイプ | conference paper | |||||||||||||||
| 出版タイプ | ||||||||||||||||
| 出版タイプ | VoR | |||||||||||||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||||||||||||
| 書誌情報 |
p. 1-18, 発行日 2022 |
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| 会議記述 | ||||||||||||||||
| 会議名 | Computability Theory and Foundations of Mathematics | |||||||||||||||
| 言語 | en | |||||||||||||||
| 開催国 | SGP | |||||||||||||||
