The Extent of Computation in Malament-Hogarth Spacetimes.
We analyse the extent of possible computations following Hogarth ([2004]) conducted in Malament-Hogarth (MH) spacetimes, and Etesi and Németi ([2002]) in the special subclass containing rotating Kerr black holes. Hogarth ([1994]) had shown that any arithmetic statement could be resolved in a suitabl...
| Publicado en: | British Journal for the Philosophy of Science Vol. 59; no. 4; pp. 659 - 675 |
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| Formato: | Artículo |
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University of Chicago Press
Dec2008
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=35946065&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 35946065 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00070882 BPL jtl: British Journal for the Philosophy of Science issn: 00070882 maglogo: N pubinfo: dt: Dec2008 vid: 59 iid: 4 pid: 415 pub: University of Chicago Press artinfo: ui: 35946065 10.1093/bjps/axn031 ppf: 659 ppct: 16 formats: tig: atl: The Extent of Computation in Malament-Hogarth Spacetimes. aug: au: Welch, P. D. affil: School of Mathematics, University of Bristol, Bristol, England BS8 1TW su: Space-time codes Supermassive black holes Arithmetic Number theory Question (Logic) sug: subj: Space-time codes Supermassive black holes Arithmetic Number theory Question (Logic) ab: We analyse the extent of possible computations following Hogarth ([2004]) conducted in Malament-Hogarth (MH) spacetimes, and Etesi and Németi ([2002]) in the special subclass containing rotating Kerr black holes. Hogarth ([1994]) had shown that any arithmetic statement could be resolved in a suitable MH spacetime. Etesi and Németi ([2002]) had shown that some relations ∀∃ on natural numbers that are neither universal nor co-universal, can be decided in Kerr spacetimes, and had asked specifically as to the extent of computational limits there. The purpose of this note is to address this question, and further show that MH spacetimes can compute far beyond the arithmetic: effectively Borel statements (so hyperarithmetic in second-order number theory, or the structure of analysis) can likewise be resolved: Theorem A. If H is any hyperarithmetic predicate on integers, then there is an MH spacetime in which any query ? n ϵ H ? can be computed. In one sense this is best possible, as there is an upper bound to computational ability in any spacetime, which is thus a universal constant of that spacetime. Theorem C. Assuming the (modest and standard) requirement that spacetime manifolds be paracompact and Hausdorff, for any spacetime M there will be a countable ordinal upper bound, w(M), on the complexity of questions in the Borel hierarchy computable in it. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2008 holdings: @attributes: islocal: N |
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