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  1. Deciding Arithmetic Using SAD Computers.Mark Hogarth - 2004 - British Journal for the Philosophy of Science 55 (4):681-691.
    Presented here is a new result concerning the computational power of so-called SADn computers, a class of Turing-machine-based computers that can perform some non-Turing computable feats by utilising the geometry of a particular kind of general relativistic spacetime. It is shown that SADn can decide n-quantifier arithmetic but not (n+1)-quantifier arithmetic, a result that reveals how neatly the SADn family maps into the Kleene arithmetical hierarchy. Introduction Axiomatising computers The power of SAD computers Remarks regarding the concept of computability.
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  • Trial and Error Predicates and the Solution to a Problem of Mostowski.Hilary Putnam - 1965 - Journal of Symbolic Logic 30 (1):49-57.
  • Infinite Pains: The Trouble with Supertasks.John Earman & John Norton - 1996 - In Adam Morton & Stephen P. Stich (eds.), Benacerraf and His Critics. Blackwell. pp. 11--271.
  • Limiting Recursion.E. Mark Gold - 1965 - Journal of Symbolic Logic 30 (1):28-48.
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  • Forever is a Day: Supertasks in Pitowsky and Malament-Hogarth Spacetimes.John Earman & John D. Norton - 1993 - Philosophy of Science 60 (1):22-42.
    The standard theory of computation excludes computations whose completion requires an infinite number of steps. Malament-Hogarth spacetimes admit observers whose pasts contain entire future-directed, timelike half-curves of infinite proper length. We investigate the physical properties of these spacetimes and ask whether they and other spacetimes allow the observer to know the outcome of a computation with infinitely many steps.
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  • Non-Turing Computers and Non-Turing Computability.Mark Hogarth - 1994 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1994:126-138.
    A true Turing machine requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime, but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar to our world. But curiously enough-and this is (...)
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  • Relativistic Computers and the Turing Barrier.István Németi & Gyula Dávid - 2006 - Journal of Applied Mathematics and Computation 178:118--42.
  • Non-Turing Computations Via Malament-Hogarth Space-Times.Gábor Etesi & István Németi - 2002 - International Journal of Theoretical Physics 41:341--70.
  • The Physical Church Thesis and Physical Computational Complexity.Itamar Pitowski - 1990 - Iyyun 39:81-99.
  • Non-Turing Computers and Non-Turing Computability.Mark Hogarth - 1994 - Psa 1994:126--138.
    A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...)
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  • Does General Relativity Allow an Observer to View an Eternity in a Finite Time?Mark Hogarth - 1992 - Foundations Of Physics Letters 5:173--181.
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