Journal of Symbolic Logic

Almost everywhere domination

Natasha L. Dobrinen and Stephen G. Simpson

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Abstract

A Turing degree a is said to be almost everywhere dominating if, for almost all X∈ 2ω with respect to the “fair coin” probability measure on 2ω, and for all g : ω→ω Turing reducible to X, there exists f : ω→ω of Turing degree a which dominates g. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly defined classes of Turing degrees. We relate this problem to some questions in the reverse mathematics of measure theory.

Article information

Source
J. Symbolic Logic, Volume 69, Issue 3 (2004), 914-922.

Dates
First available in Project Euclid: 4 October 2004

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1096901775

Digital Object Identifier
doi:10.2178/jsl/1096901775

Mathematical Reviews number (MathSciNet)
MR2078930

Zentralblatt MATH identifier
1075.03021

Citation

Dobrinen, Natasha L.; Simpson, Stephen G. Almost everywhere domination. J. Symbolic Logic 69 (2004), no. 3, 914--922. doi:10.2178/jsl/1096901775. https://projecteuclid.org/euclid.jsl/1096901775


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References

  • Douglas K. Brown, Mariagnese Giusto, and Stephen G. Simpson Vitali's theorem and WWKL, Archive for Mathematical Logic, vol. 41 (2002), pp. 191--206.
  • Paul R. Halmos Measure theory, Van Nostrand,1950.
  • Peter G. Hinman Recursion-theoretic hierarchies, Perspectives in Mathematical Logic, Springer-Verlag,1978.
  • Steven M. Kautz Degrees of random sets, Ph.D. thesis, Cornell University,1991.
  • Stuart A. Kurtz Randomness and genericity in the degrees of unsolvability, Ph.D. thesis, University of Illinois at Urbana-Champaign,1981.
  • Donald A. Martin Classes of recursively enumerable sets and degrees of unsolvability, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, vol. 12 (1966), pp. 295--310.
  • Gerald E. Sacks Measure-theoretic uniformity in recursion theory and set theory, Transactions of the American Mathematical Society, vol. 142 (1969), pp. 381--420.
  • W. Sieg (editor) Logic and computation, Contemporary Mathematics, American Mathematical Society,1990.
  • S. G. Simpson (editor) Reverse mathematics 2001, Lecture Notes in Logic, Association for Symbolic Logic,2004, to appear.
  • Stephen G. Simpson $\Pi^0_1$ sets and models of $\mathsfWKL_0$, in [?], preprint, April 2000, 29 pages, to appear.
  • Robert I. Soare Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag,1987.
  • Xiaokang Yu Measure theory in weak subsystems of second order arithmetic, Ph.D. thesis, Pennsylvania State University,1987.
  • Xiaokang Yu and Stephen G. Simpson Measure theory and weak König's lemma, Archive for Mathematical Logic, vol. 30 (1990), pp. 171--180.