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ファイル | 記述 | サイズ | フォーマット | |
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00294527-2010-020.pdf | 208.8 kB | Adobe PDF | 見る/開く |
タイトル: | An Extension of van Lambalgen's Theorem to Infinitely Many Relative 1-Random Reals |
著者: | Miyabe, Kenshi |
著者名の別形: | 宮部, 賢志 |
キーワード: | van Lambalgen’s Theorem martingale high Omega operator |
発行日: | Jul-2010 |
出版者: | University of Notre Dame |
誌名: | Notre Dame Journal of Formal Logic |
巻: | 51 |
号: | 3 |
開始ページ: | 337 |
終了ページ: | 349 |
抄録: | Van Lambalgen’s Theorem plays an important role in algorithmic randomness, especially when studying relative randomness. In this paper we extend van Lambalgen’s Theorem by considering the join of infinitely many reals which are random relative to each other. In addition, we study computability of the reals in the range of Omega operators. It is known that Ωϕ′ is high. We extend this result to that Ωϕ(n) is highn. We also prove that there exists A such that, for each n, the real ΩAM is highn for some universal Turing machine M by using the extended van Lambalgen’s Theorem. |
著作権等: | 2010 © University of Notre Dame |
URI: | http://hdl.handle.net/2433/131806 |
DOI(出版社版): | 10.1215/00294527-2010-020 |
出現コレクション: | 学術雑誌掲載論文等 |
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