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Conference on Computability in Europe

CiE 2018: Sailing Routes in the World of Computation pp 307–317Cite as

The Complexity of Tukey Types and Cofinal Types

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10936))

Abstract

This paper studies how difficult it is to determine whether two computable partial orders share the same Tukey type and the same cofinal type. For Tukey types, we show the index set is \(\mathbf {0}^{(3)}\). For cofinal types, the we shows the index set is computable from \(\mathbf {0}^{(4)}\). This is in sharp contrast to the isomorphism problem for computable partial orders, which is \(\varSigma ^1_1\).

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Authors and Affiliations

  1. Cork Institute of Technology, Cork, Ireland

    Marie Nicholson

Authors
  1. Marie Nicholson
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Correspondence to Marie Nicholson .

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Editors and Affiliations

  1. Kiel University, Kiel, Germany

    Florin Manea

  2. Queens College, CUNY, Queens, New York, USA

    Russell G. Miller

  3. Kiel University, Kiel, Germany

    Dirk Nowotka

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Nicholson, M. (2018). The Complexity of Tukey Types and Cofinal Types. In: Manea, F., Miller, R., Nowotka, D. (eds) Sailing Routes in the World of Computation. CiE 2018. Lecture Notes in Computer Science(), vol 10936. Springer, Cham. https://doi.org/10.1007/978-3-319-94418-0_31

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  • DOI: https://doi.org/10.1007/978-3-319-94418-0_31

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-94417-3

  • Online ISBN: 978-3-319-94418-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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