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Mass problems associated with effectively closed sets
http://hdl.handle.net/10097/00106145
http://hdl.handle.net/10097/00106145011b72f7-5bb0-4d7c-bf5d-d2336eb72026
| Item type | [ELS]紀要論文 / Departmental Bulletin Paper(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2017-04-07 | |||||
| タイトル | ||||||
| タイトル | Mass problems associated with effectively closed sets | |||||
| 言語 | en | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
| 資源タイプ | departmental bulletin paper | |||||
| アクセス権 | ||||||
| アクセス権 | metadata only access | |||||
| アクセス権URI | http://purl.org/coar/access_right/c_14cb | |||||
| 雑誌書誌ID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA00863953 | |||||
| 論文名よみ | ||||||
| タイトル | Mass problems associated with effectively closed sets | |||||
| 著者 |
Simpson, Stephen G.
× Simpson, Stephen G. |
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| 著者所属(英) | ||||||
| 言語 | en | |||||
| 値 | Department of Mathematics, The Pennsylvania State University | |||||
| 記事種別(英) | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | Article | |||||
| 抄録(英) | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | The study of mass problems and Muchnik degrees was originally motivated by Kolmogorov's non-rigorous 1932 interpretation of intuitionism as a calculus of problems. The purpose of this paper is to summarize recent investigations into the lattice of Muchnik degrees of nonempty effectively closed sets in Euclidean space. Let $\mathcal{E}_\mathrm{w}$ be this lattice. We show that $\mathcal{E}_\mathrm{w}$ provides an elegant and useful framework for the classification of certain foundationally interesting problems which are algorithmically unsolvable. We exhibit some specific degrees in $\mathcal{E}_\mathrm{w}$ which are associated with such problems. In addition, we present some structural results concerning the lattice $\mathcal{E}_\mathrm{w}$. One of these results answers a question which arises naturally from the Kolmogorov interpretation. Finally, we show how $\mathcal{E}_\mathrm{w}$ can be applied in symbolic dynamics, toward the classification of tiling problems and $\boldsymbol{Z}^d$-subshifts of finite type. | |||||
| 書誌情報 |
東北數學雜誌. Second series en : Tohoku mathematical journal. Second series 巻 63, 号 4, p. 489-517, 発行日 2011-12-01 |
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| URL | ||||||
| 識別子 | J-STAGE | https://www.jstage.jst.go.jp/article/tmj/63/4/63_489/_article/-char/ja | |||||
| 識別子タイプ | URI | |||||
| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 00408735 | |||||
