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2006 A C.E. Real That Cannot Be SW-Computed by Any Ω Number
George Barmpalias, Andrew E. M. Lewis
Notre Dame J. Formal Logic 47(2): 197-209 (2006). DOI: 10.1305/ndjfl/1153858646


The strong weak truth table (sw) reducibility was suggested by Downey, Hirschfeldt, and LaForte as a measure of relative randomness, alternative to the Solovay reducibility. It also occurs naturally in proofs in classical computability theory as well as in the recent work of Soare, Nabutovsky, and Weinberger on applications of computability to differential geometry. We study the sw-degrees of c.e. reals and construct a c.e. real which has no random c.e. real (i.e., Ω number) sw-above it.


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George Barmpalias. Andrew E. M. Lewis. "A C.E. Real That Cannot Be SW-Computed by Any Ω Number." Notre Dame J. Formal Logic 47 (2) 197 - 209, 2006.


Published: 2006
First available in Project Euclid: 25 July 2006

MathSciNet: MR2240619
zbMATH: 1113.03035
Digital Object Identifier: 10.1305/ndjfl/1153858646

Primary: 03D80
Secondary: 03D15

Keywords: c.e. reals , randomness , sw reducibility

Rights: Copyright © 2006 University of Notre Dame


Vol.47 • No. 2 • 2006
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