DEMUTH’S PATH TO RANDOMNESS.
Osvald Demuth (1936–1988) studied constructive analysis from the viewpoint of the Russian school of constructive mathematics. In the course of his work he introduced various notions of effective null set which, when phrased in classical language, yield a number of major algorithmic randomness notion...
| Publicado en: | Bulletin of Symbolic Logic Vol. 21; no. 3; pp. 270 - 306 |
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| Autores principales: | , , |
| Formato: | Artículo |
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Cambridge University Press
Sep2015
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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=109455875&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 109455875 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 10798986 1BA jtl: Bulletin of Symbolic Logic issn: 10798986 maglogo: N pubinfo: dt: Sep2015 vid: 21 iid: 3 pid: 15979 pub: Cambridge University Press artinfo: ui: 109455875 10.1017/bsl.2015.24 ppf: 270 ppct: 36 formats: tig: atl: DEMUTH’S PATH TO RANDOMNESS. aug: au: KUČERA, ANTONÍN NIES, ANDRÉ PORTER, CHRISTOPHER P. affil: FACULTY OF MATHEMATICS AND PHYSICS CHARLES UNIVERSITY IN PRAGUE PRAGUE, CZECH REPUBLIC E-mail: kucera@mbox.ms.mff.cuni.cz DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF AUCKLAND AUCKLAND, NEW ZEALAND E-mail: andre@cs.auckland.ac.nz DEPARTMENT OF MATHEMATICS UNIVERSITY OF FLORIDA GAINESVILLE FL 32611-8105, USA E-mail: cp@cpporter.com su: Constructive mathematics Mathematical logic Computable functions Set theory Algebra sug: subj: Constructive mathematics Mathematical logic Computable functions Set theory Algebra ab: Osvald Demuth (1936–1988) studied constructive analysis from the viewpoint of the Russian school of constructive mathematics. In the course of his work he introduced various notions of effective null set which, when phrased in classical language, yield a number of major algorithmic randomness notions. In addition, he proved several results connecting constructive analysis and randomness that were rediscovered only much later.In this paper, we trace the path that took Demuth from his constructivist roots to his deep and innovative work on the interactions between constructive analysis, algorithmic randomness, and computability theory. We will focus specifically on (i) Demuth’s work on the differentiability of Markov computable functions and his study of constructive versions of the Denjoy alternative, (ii) Demuth’s independent discovery of the main notions of algorithmic randomness, as well as the development of Demuth randomness, and (iii) the interactions of truth-table reducibility, algorithmic randomness, and semigenericity in Demuth’s work. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y dt: @attributes: year: 2015 holdings: @attributes: islocal: N |
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