Journal Article

Deciding Arithmetic Using <i>SAD</i> Computers

Mark Hogarth

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 55, issue 4, pages 681-691
Published in print December 2004 | ISSN: 0007-0882
Published online December 2004 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/55.4.681
Deciding Arithmetic Using SAD Computers

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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

Journal Article.  0 words. 

Subjects: Philosophy of Science ; Science and Mathematics

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