Mark Hogarth
Cambridge University
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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DOI 10.1093/bjps/55.4.681
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References found in this work BETA

Computability and Logic.G. S. Boolos & R. C. Jeffrey - 1977 - British Journal for the Philosophy of Science 28 (1):95-95.
Theory of Recursive Functions and Effective Computability.Hartley Rogers - 1971 - Journal of Symbolic Logic 36 (1):141-146.

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Citations of this work BETA

Computation in Physical Systems.Gualtiero Piccinini - 2010 - Stanford Encyclopedia of Philosophy.
The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
SAD Computers and Two Versions of the Church–Turing Thesis.Tim Button - 2009 - British Journal for the Philosophy of Science 60 (4):765-792.

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