Unique Existence and Computability in Constructive Reverse Mathematics

  • Hajime Ishihara
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)


We introduce, and show the equivalences among, relativized versions of Brouwer’s fan theorem for detachable bars (FAN), weak König 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 \(f(\alpha) = \inf f(\{0,1\}^\mathbf{N})\), is equivalent to some computably relativized version of FAN, WKL! and LPL!.


unique existence computability Brouwer’s fan theorem weak König lemma constructive mathematics reverse mathematics 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Hajime Ishihara
    • 1
  1. 1.School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa 923-1292Japan

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