A REAL OF STRICTLY POSITIVE EFFECTIVE PACKING DIMENSION THAT DOES NOT COMPUTE A REAL OF EFFECTIVE PACKING ONE.
Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [14], where the author constructs a Turing degree of non-integral Hausdorff-dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly posit...
| Publicado en: | Journal of Symbolic Logic Vol. 77; no. 2; pp. 447 - 475 |
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| Formato: | Artículo |
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Cambridge University Press
Jun2012
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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=76263564&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 76263564 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00224812 3TY jtl: Journal of Symbolic Logic issn: 00224812 maglogo: N pubinfo: dt: Jun2012 vid: 77 iid: 2 pid: 15979 pub: Cambridge University Press artinfo: ui: 76263564 10.2178/jsl/1333566632 ppf: 447 ppct: 28 formats: tig: atl: A REAL OF STRICTLY POSITIVE EFFECTIVE PACKING DIMENSION THAT DOES NOT COMPUTE A REAL OF EFFECTIVE PACKING ONE. aug: au: Conidis, Chris J. affil: Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3GI, Canada su: Measure theory Hausdorff measures Algebraic topology Ring theory Fractals sug: subj: Measure theory Hausdorff measures Algebraic topology Ring theory Fractals keyword: algorithmic randomness Computability theory effective fractal dimension Kolmogorov complexity ab: Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [14], where the author constructs a Turing degree of non-integral Hausdorff-dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one (on the other hand, it is known via [10, 3, 7] that every real of strictly positive effective Hausdorff dimension computes reals whose effective packing dimensions are arbitrarily close to, but not necessarily equal to, one). pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2012 holdings: @attributes: islocal: N |
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