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http://hdl.handle.net/10119/7876
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| Title: | Unique Existence and Computability in Constructive Reverse Mathematics |
| Authors: | Ishihara, Hajime |
| Keywords: | unique existence
computability
Brouwer's fan theorem
weak Konig lemma
constructive mathematics
reverse mathematics |
| Issue Date: | 2007 |
| Publisher: | Springer |
| Magazine name: | Lecture Notes in Computer Science |
| Volume: | 4497 |
| Start page: | 368 |
| End page: | 377 |
| DOI: | 10.1007/978-3-540-73001-9_38 |
| Abstract: | We introduce, and show the equivalences among, relativized versions of Brouwer's fan theorem for detachable bars (FAN), weak Konig lemma with a uniqueness hypothesis (WKL!), and the longest path lemma with a uniqueness hypothesis (LPL!) in the spirit of constructive reverse mathematics. We prove that a computable version of minimum principle: if f is a real valued computable uniformly continuous function with at most one minimum on {0,1}^N , then there exists a computable α in {0,1}^N such that f(α) = inf f({0,1}^N) is equivalent to some computably relativized version of FAN, WKL! and LPL!. |
| Rights: | This is the author-created version of Springer, Hajime Ishihara, Lecture Notes in Computer Science, 4497, 2007, 368-377. The original publication is available at www.springerlink.com, http://dx.doi.org/10.1007/978-3-540-73001-9_38 |
| URI: | http://hdl.handle.net/10119/7876 |
| Material Type: | author |
| Appears in Collections: | b10-1. 雑誌掲載論文 (Journal Articles)
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| C11154.pdf | | 207Kb | Adobe PDF | View/Open |
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