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b10-1. 雑誌掲載論文 >
このアイテムの引用には次の識別子を使用してください:
http://hdl.handle.net/10119/14707
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| タイトル: | On principles between ∑1- and ∑2-induction, and monotone enumerations |
| 著者: | Kreuzer, Alexander P.
Yokoyama, Keita |
| キーワード: | fragments of arithmetics
reverse mathematics
Ackermann function
Paris Harrington theorem
ordinal numbers |
| 発行日: | 2016-06-30 |
| 出版者: | World Scientific Publishing |
| 誌名: | Journal of Mathematical Logic |
| 巻: | 16 |
| 号: | 1 |
| 開始ページ: | 1650004-1 |
| 終了ページ: | 1650004-21 |
| DOI: | 10.1142/S0219061316500045 |
| 抄録: | We show that many principles of first-order arithmetic, previously only known to lie strictly between ∑_1-induction and ∑_2-induction, are equivalent to the well-foundedness of ω^ω. Among these principles are the iteration of partial functions (P∑_1) of Hajek and Paris, the bounded monotone enumerations principle (non-iterated, BME_1) by Chong, Slaman, and Yang, the relativized Paris-Harrington principle for pairs, and the totality of the relativized Ackermann-Peter function. With this we show that the well-foundedness of ω^ω is a far more widespread than usually suspected. Further, we investigate the k-iterated version of the bounded monotone iterations principle (BME_k), and show that it is equivalent to the well-foundedness of the k + 1-height -tower ω⋰ω. |
| Rights: | Electronic version of an article published as Journal of Mathematical Logic, 16(1), 2016, 1650004-1-1650004-21. DOI:10.1142/S0219061316500045. Copyright World Scientific Publishing Company, http://dx.doi.org/10.1142/S0219061316500045 |
| URI: | http://hdl.handle.net/10119/14707 |
| 資料タイプ: | author |
| 出現コレクション: | b10-1. 雑誌掲載論文 (Journal Articles)
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このアイテムのファイル:
| ファイル |
記述 |
サイズ | 形式 |
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| 22907.pdf | | 513Kb | Adobe PDF | 見る/開く |
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