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Infinite time Turing machines

  • Joel David Hamkins (a1) and Andy Lewis (a2)

We extend in a natural way the operation of Turing machines to infinite ordinal time, and investigate the resulting supertask theory of computability and decidability on the reals. Every set. for example, is decidable by such machines, and the semi-decidable sets form a portion of the sets. Our oracle concept leads to a notion of relative computability for sets of reals and a rich degree structure, stratified by two natural jump operators.

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[Ear & Nor] John Earman and John D. Norton , Forever is a day: supertasks in Pitowski and Malament-Hogarth spacetimes, Philosophy of Science, vol. 60 (1993), no. 1, pp. 2242.

[Hog92] Hogarth , Does general relativity allow an observer to view an eternity in a finite time?, Foundations of Physics Letters, vol. 5 (1992), pp. 173181.

[Sacks] Gerald E. Sacks , Higher Recursion Theory, Springer Verlag Publishing Company, New York, 1990.

[Soare] Robert I. Soare , Recursively Enumerable Sets and Degrees, Springer Verlag Publishing Company, New York, 1987.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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