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Infinite-Time Turing Machines and Borel Reducibility

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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

In this document I will outline a couple of recent developments, due to Joel Hamkins, Philip Welch and myself, in the theory of infinite-time Turing machines. These results were obtained with the idea of extending the scope of the study of Borel equivalence relations, an area of descriptive set theory. I will introduce the most basic aspects of Borel equivalence relations, and show how infinite-time computation may provide insight into this area.

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References

  1. Hamkins, J.D., Lewis, A.: Infinite time Turing machines. J. Symbolic Logic 65(2), 567–604 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  2. Welch, P.D.: Minimality arguments for infinite time Turing degrees. In: Sets and proofs (Leeds, 1997). London Math. Soc. Lecture Note Ser., vol. 258, pp. 425–436. Cambridge Univ. Press, Cambridge (1999)

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  3. Deolalikar, V., Hamkins, J.D., Schindler, R.: P ≠ NP ∩ co-NP for infinite time Turing machines. J. Logic Comput. 15(5), 577–592 (2005)

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  4. Friedman, H., Stanley, L.: A Borel reducibility theory for classes of countable structures. J. Symbolic Logic 54(3), 894–914 (1989)

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  5. Hjorth, G., Kechris, A.S.: Borel equivalence relations and classifications of countable models. Annals of pure and applied logic 82(3), 221–272 (1996)

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  6. Thomas, S.: Countable Borel equivalence relations. Online somewhere (2007)

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  7. Adams, S., Kechris, A.: Linear algebraic groups and countable Borel equivalence relations. Journal of the American mathematical society 13(4), 909–943 (2000)

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Author information

Authors and Affiliations

  1. The City University of New York, USA

    Samuel Coskey

Authors
  1. Samuel Coskey
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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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Coskey, S. (2009). Infinite-Time Turing Machines and Borel Reducibility. 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_14

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  • DOI: https://doi.org/10.1007/978-3-642-03073-4_14

  • 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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