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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/10119/11577
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| タイトル: | Reverse mathematics and Peano categoricity |
| 著者: | Simpson, Stephen G.
Yokoyama, Keita |
| キーワード: | Reverse mathematics
second-order arithmetic
Peano system
proof-theory
second-order logic |
| 発行日: | 2012-10-27 |
| 出版者: | Elsevier |
| 誌名: | Annals of Pure and Applied Logic |
| 巻: | 164 |
| 号: | 3 |
| 開始ページ: | 284 |
| 終了ページ: | 293 |
| DOI: | 10.1016/j.apal.2012.10.014 |
| 抄録: | We investigate the reverse-mathematical status of several theorems to the effect that the natural number system is second-order categorical. One of our results is as follows. Define a system to be a triple A,i,f such that A is a set and i ∈ A and f : A→A. A subset X⊆A is said to be inductive if i ∈ X and ∀a (a ∈ X⇒f(a) ∈ X). The system A,i,f is said to be inductive if the only inductive subset of A is A itself. Define a Peano system to be an inductive system such that f is one-to-one and i ∉ the range of f. The standard example of a Peano system is N,0,S where N={0,1,2,…,n,…} = the set of natural numbers and S:N→N is given by S(n) = n+1 for all n ∈ N. Consider the statement that all Peano systems are isomorphic to N,0,S. We prove that this statement is logically equivalent to WKL_0 over RCA^*_0. From this and similar equivalences we draw some foundational/philosophical consequences. |
| Rights: | NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Stephen G. Simpson and Keita Yokoyama, Annals of Pure and Applied Logic, 164(3), 2012, 284-293, http://dx.doi.org/10.1016/j.apal.2012.10.014 |
| URI: | http://hdl.handle.net/10119/11577 |
| 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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