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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/10119/12317
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| タイトル: | Categorical characterizations of the natural numbers require primitive recursion |
| 著者: | Kolodziejczyk, Leszek Aleksander
Yokoyama, Keita |
| キーワード: | reverse mathematics
second-order logic
Peano system
categorical sentences
nonstandard models |
| 発行日: | 2014-10-30 |
| 出版者: | Elsevier |
| 誌名: | Annals of Pure and Applied Logic |
| 巻: | 166 |
| 号: | 2 |
| 開始ページ: | 219 |
| 終了ページ: | 231 |
| DOI: | 10.1016/j.apal.2014.10.003 |
| 抄録: | Simpson and Yokoyama [Ann. Pure Appl. Logic 164 (2013), 284–293] asked whether there exists a characterization of the natural numbers by asecond-order sentence which is provably categorical in the theory RCA^*_0. Weanswer in the negative, showing that for any characterization of the natural numbers which is provably true in WKL^*_0, the categoricity theorem implies Σ^0_1induction. On the other hand, we show that RCA^*_0 does make it possible to characterize the natural numbers categorically by means of a set of second-order sentences.We also show that a certain Π^1_2-conservative extension of RCA^*_0 admits a provably categorical single-sentence characterization of the naturals,but each such characterization has to be inconsistent with WKL^*_0 +superexp. |
| Rights: | NOTICE: This is the author's version of a work accepted for publication by Elsevier. Leszek Aleksander Kolodziejczyk and Keita Yokoyama, Annals of Pure and Applied Logic, 166(2), 2014, 219-231, http://dx.doi.org/10.1016/j.apal.2014.10.003 |
| URI: | http://hdl.handle.net/10119/12317 |
| 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:
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| 21161.pdf | | 98Kb | Adobe PDF | 見る/開く |
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