Hogarth, M. (2004) Deciding arithmetic using SAD computers. British Journal for the Philosophy of Science, 55(4), pp. 681-691. (doi: 10.1093/bjps/55.4.681)
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Publisher's URL: http://dx.doi.org/10.1093/bjps/55.4.681
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.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Hogarth, Dr Mark |
| Authors: | Hogarth, M. |
| Subjects: | B Philosophy. Psychology. Religion > BC Logic Q Science > QA Mathematics |
| College/School: | College of Arts & Humanities > School of Humanities > Philosophy |
| Journal Name: | British Journal for the Philosophy of Science |
| ISSN: | 0007-0882 |
| ISSN (Online): | 1464-3537 |
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