Titlebook: Logicism, Intuitionism, and Formalism; What Has Become of T Sten Lindström,Erik Palmgren,Viggo Stoltenberg-Han Book 2009 Springer Science+B

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Dini’s Theorem in the Light of Reverse Mathematicsiformly continuous real-valued functions whose limit is uniformly continuous. By showing that it is equivalent to Brouwer’s fan theorem for detachable bars, we provide Dini’s theorem with a classification in the constructive reverse mathematics recently propagated by Ishihara. If the functions occur

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Relativization of Real Numbers to a Universeshow that the class R(Ϝptime) of real numbers, obtained by relativizing to the class F Ptime of polynomial time computable functions, is a proper subclass of the class R(ε) of real numbers, obtained by relativizing to the class ε of elementary functions. We show the Cauchy completeness of relativize

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Program Extraction in Constructive Analysis). The goal is to set up things in such a way that realistically executable programs can be extracted from proofs. This is carried out for (1) the Intermediate Value Theorem and (2) the existence of a continuous inverse to a monotonically increasing continuous function. Using the Minlog proof assist

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