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A Minimal Pair in the Quotient Structure M/NCup

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Computation and Logic in the Real World (CiE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4497))

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Abstract

In this paper, we prove the existence of a minimal pair of c.e. degrees a and b such that both of them are cuppable, and no incomplete c.e. degree can cup both of them to 0′. As a consequence, [a] and [b] form a minimal pair in M/NCup, the quotient structure of the cappable degrees modulo noncuppable degrees. We also prove that the dual of Lempp’s conjecture is true.

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Author information

Authors and Affiliations

  1. School of Information Science and Technology, Beijing Normal University, Beijing 100875, People’s Republic of China

    Rongfang Bie

  2. Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Republic of Singapore

    Guohua Wu

Authors
  1. Rongfang Bie
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  2. Guohua Wu
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Editor information

Editors and Affiliations

  1. Dept. of Pure Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Institue for Logic, Language and Computation (ILLC), Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, TV Amsterdam, The Netherlands

    Benedikt Löwe

  3. Dipartimento di Scienze Matematiche ed Informatiche “R. Magari”, University of Siena, 53100, Siena, Italy

    Andrea Sorbi

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Bie, R., Wu, G. (2007). A Minimal Pair in the Quotient Structure M/NCup . In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_6

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  • DOI: https://doi.org/10.1007/978-3-540-73001-9_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73000-2

  • Online ISBN: 978-3-540-73001-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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