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International Workshop on Computer Science Logic

CSL 2000: Computer Science Logic pp 512–526Cite as

Elementary Choiceless Constructive Analysis

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1862))

Abstract

Existential statements seem to admit a constructive proof without countable choice only if the object to be constructed is uniquely determined, or is intended as an approximate solution of the problem in question. This conjecture is substantiated by re-examining some basic tools of mathematical analysis from a choice-free constructive point of view, starting from Dedekind cuts as an appropriate notion of real numbers. As a complement, the question whether densely defined continuous functions do approximate intermediate values is reduced to connectivity properties of the corresponding domains.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333, München, Germany

    Peter M. Schuster

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  1. Peter M. Schuster
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Department of Biology, Boston College, Fulton Hall 410B, Chestnut Hill, MA, 02467, USA

    Peter G. Clote

  2. Mathematisches Institut, Ludwig-Maximilian-Universität München, Theresienstr. 39, 80333, München, Germany

    Helmut Schwichtenberg

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© 2000 Springer-Verlag Berlin Heidelberg

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Schuster, P.M. (2000). Elementary Choiceless Constructive Analysis. In: Clote, P.G., Schwichtenberg, H. (eds) Computer Science Logic. CSL 2000. Lecture Notes in Computer Science, vol 1862. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44622-2_35

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  • DOI: https://doi.org/10.1007/3-540-44622-2_35

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67895-3

  • Online ISBN: 978-3-540-44622-4

  • eBook Packages: Springer Book Archive

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