Deciding arithmetic using SAD computers

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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Gualtiero Piccinini (2011). The Physical Church–Turing Thesis: Modest or Bold? British Journal for the Philosophy of Science 62 (4):733 - 769.
Tim Button (2009). SAD Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
P. D. Welch (2008). The Extent of Computation in Malament–Hogarth Spacetimes. British Journal for the Philosophy of Science 59 (4):659-674.

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