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Infinite time Turing machines

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

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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[Bar]Barwise John, Admissible Set Theory, Springer Verlag Publishing Company, New York, 1990.
[Dub]Dubose Derrick Albert, The Equivalency of Determinacy and Iterated Sharps, this Journal, vol. 55 (1980), no. 2, pp. 502510.
[Ear]Earman John, Bangs, crunches, whimpers and shrieks: singularities and acausalities in relativistic spacetimes, The Clarendon Press, Oxford University Press, New York, 1995.
[Ear & Nor]Earman John and Norton John D., Forever is a day: supertasks in Pitowski and Malament-Hogarth spacetimes, Philosophy of Science, vol. 60 (1993), no. 1, pp. 2242.
[Fef & Spc]Feferman Solomon and Spector C., Incompleteness along paths in progressions of theories, this Journal, vol. 27 (1962), pp. 383390.
[Hog94]Hogarth, Non-Turing computers and non-Turing computability, PSA 1994, Vol I East Lansing: Philosohpy of Science Association (Hull D., Forbes M., and Burian R.B, editors), pp. 126138.
[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.
[Mos]Moschovakis Yiannis Nicholas, Descriptive Set Theory, North-Holland Publishing Company, New York, 1980.
[Pit]Pitowsky, The physical Church Thesis and Physical computational complexity, Iyyun, vol. 39 (1990), pp. 8199.
[Sacks]Sacks Gerald E., Higher Recursion Theory, Springer Verlag Publishing Company, New York, 1990.
[Soare]Soare Robert I., Recursively Enumerable Sets and Degrees, Springer Verlag Publishing Company, New York, 1987.
[Thom]Thomson, Tasks and Super-tasks, Analysis, vol. XV (19541955), pp. 113.
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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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