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A Generalised Dynamical System, Infinite Time Register Machines, and \(\Pi^1_1\)-CA0

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Models of Computation in Context (CiE 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6735))

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Abstract

We identify a number of theories of strength that of \(\Pi^1_1\)-CA0. In particular: (a) the theory that the set of points attracted to the origin in a generalised transfinite dynamical system of any n-dimensional integer torus exists; (b) the theory asserting that for any Z ⊆ ω and n, the halting set \(H^Z_n \)of infinite time n-register machine with oracle Z exists.

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References

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Peter Koepke

  2. School of Mathematics, University of Bristol, Clifton, Bristol, BS8 1TW, United Kingdom

    Philip D. Welch

Authors
  1. Peter Koepke
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  2. Philip D. Welch
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Editor information

Editors and Affiliations

  1. Institute for Logic, Language and Computation, University of Amsterdam, 1090, Amsterdam, GE, The Netherlands

    Benedikt Löwe

  2. Department of Mathematics, University of Oslo, 0316, Oslo, Norway

    Dag Normann

  3. Department of Mathematical Logic and Applications, Sofia University, 1164, Sofia, Bulgaria

    Ivan Soskov  & Alexandra Soskova  & 

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© 2011 Springer-Verlag Berlin Heidelberg

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Koepke, P., Welch, P.D. (2011). A Generalised Dynamical System, Infinite Time Register Machines, and \(\Pi^1_1\)-CA0 . In: Löwe, B., Normann, D., Soskov, I., Soskova, A. (eds) Models of Computation in Context. CiE 2011. Lecture Notes in Computer Science, vol 6735. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21875-0_16

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  • DOI: https://doi.org/10.1007/978-3-642-21875-0_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-21874-3

  • Online ISBN: 978-3-642-21875-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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