论文信息 - Almost everywhere domination

Almost everywhere domination

AT uring degreea is said to be almost everywhere dominating if, for almost all X 2 2 ! with respect to the \fair coin" probability measure on 2 ! ,a nd for allg : ! ! ! Turing reducible to X ,t here existsf : ! ! ! of Turing degree a which dominates g. We study the problem of characterizing the almost everywhere dominating Turing degrees and other, similarly dened classes of Turing degrees. We relate this problem to some questions in the reverse mathematics of measure theory.

Stephen G. Simpson | S. G. Simpson | Natasha Dobrinen | Natasha Dobrinen

[1] Wilfried Sieg. Logic and Computation , 1990 .

[2] Stephen G. Simpson,et al. Π 01 Sets and Models of WKL 0 , 2000 .

[3] Donald A. Martin,et al. Classes of Recursively Enumerable Sets and Degrees of Unsolvability , 1966 .

[4] Steven M. Kautz. Degrees of random sets , 1991 .

[5] Stephen G. Simpson,et al. Vitali's Theorem and WWKL , 2002, Arch. Math. Log..

[6] Xiaokang Yu,et al. Lebesgue Convergence Theorems and Reverse Mathematics , 1994, Math. Log. Q..

[7] Xiaokang Yu,et al. Measure theory and weak König's lemma , 1990, Arch. Math. Log..

[8] G. Sacks. Measure-theoretic uniformity in recursion theory and set theory , 1969 .

[9] R. Soare. Recursively enumerable sets and degrees , 1987 .

[10] Xiaokang Yu. A Study of Singular Points and Supports of Measures in Reverse Mathematics , 1996, Ann. Pure Appl. Log..

[11] Stephen G. Simpson,et al. Subsystems of second order arithmetic , 1999, Perspectives in mathematical logic.

[12] Xiaokang Yu,et al. Riesz Representation Theorem, Borel Measures and Subsystems of Second-Order Arithmetic , 1993, Ann. Pure Appl. Log..

[13] K. Appel. Review: Donald A. Martin, Classes of Recursively Enumerable Sets and Degrees of Unsolvability , 1967 .