Deciding arithmetic using SAD computers

Abstract
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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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.
The Extent of Computation in Malament–Hogarth Spacetimes.P. D. Welch - 2008 - British Journal for the Philosophy of Science 59 (4):659-674.

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