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\(\Sigma^0_1\) and \(\Pi^0_1\) Equivalence Structures

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Mathematical Theory and Computational Practice (CiE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5635))

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Abstract

We study computability theoretic properties of \(\Sigma _{1}^{0}\) and \(\Pi _{1}^{0}\) equivalence structures and how they differ from computable equivalence structures or equivalence structures that belong to the Ershov difference hierarchy. Our investigation includes the complexity of isomorphisms between \(\Sigma _{1}^{0}\) equivalence structures and between \(\Pi _{1}^{0}\) equivalence structures.

This research was partially supported by NSF grants DMS-0532644 and DMS-0554841. Cenzer was partially supported by DMS 652372, Harizanov was partially supported by DMS-0704256 and Jeffrey Remmel was partially supported by NSF grant DMS 0654060.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, Florida, 32611

    Douglas Cenzer

  2. Department of Mathematics, George Washington University, Washington, D.C., 20052

    Valentina Harizanov

  3. Department of Mathematics, University of California-San Diego, La Jolla, CA, 92093

    Jeffrey B. Remmel

Authors
  1. Douglas Cenzer
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  2. Valentina Harizanov
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  3. Jeffrey B. Remmel
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Editor information

Editors and Affiliations

  1. University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Klaus Ambos-Spies

  2. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, Amsterdam, TV, The Netherlands

    Benedikt Löwe

  3. Institut für Informatik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Wolfgang Merkle

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Cenzer, D., Harizanov, V., Remmel, J.B. (2009). \(\Sigma^0_1\) and \(\Pi^0_1\) Equivalence Structures. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_11

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  • DOI: https://doi.org/10.1007/978-3-642-03073-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03072-7

  • Online ISBN: 978-3-642-03073-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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