Unique Existence and Computability in Constructive Reverse Mathematics
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概要
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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!.
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