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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/7876

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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