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A finite hierarchy of the recursively enumerable real numbers

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

For any set A of natural numbers, denote by x A the corresponding real number such that A is just the set of “1” positions in its binary expansion. In this paper we characterize the number x A for some classes of recursively enumerable sets A. Applying finite injury priority methods we show that there is a d-r.e. set A such that x A is not a semi-computable real number (which corresponds to the limit of computable monotonic sequence of rational numbers) and that there is an Ω-r.e. set A such that x A can't be represented as a sum of two semi-computable real numbers.

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Authors and Affiliations

  1. Theoretische Informatik I, Fern Universität Hagen, 58084, Hagen, Germany

    Klaus Weihrauch & Xizhong Zheng

Authors
  1. Klaus Weihrauch
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  2. Xizhong Zheng
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Editor information

Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Weihrauch, K., Zheng, X. (1998). A finite hierarchy of the recursively enumerable real numbers. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055831

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  • DOI: https://doi.org/10.1007/BFb0055831

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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