Limits on jump inversion for strong reducibilities
Barbara F. Csima, Rod Downey, and Keng Meng Ng
Source: J. Symbolic Logic Volume 76, Issue 4
(2011), 1287-1296.
Abstract
We show that Sacks' and Shoenfield's analogs of jump inversion fail for both tt- and wtt-reducibilities in a strong way. In particular we show that there is a Δ02 set B >tt ∅' such that there is no c.e. set A with A' ≡wtt B. We also show that there is a Σ02 set C >tt ∅' such that there is no Δ02 set D with D' ≡wtt C.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1318338849
Digital Object Identifier: doi:10.2178/jsl/1318338849
Zentralblatt MATH identifier: 05991458
Mathematical Reviews number (MathSciNet): MR2895396
References
B. Anderson, Automorhisms of the truth-table degrees are fixed on some cone, preprint, 2008.
S. Barry Cooper, Computability theory, Chapman & Hall/CRC, Boca Raton, FL, 2004.
Mathematical Reviews (MathSciNet): MR2017461
O. Demuth, Remarks on the structure of tt-degrees based on constructive measure theory, Commentationes Mathematicae Universitatis Carolinae, vol. 29 (1988), no. 2, pp. 233–247.
Mathematical Reviews (MathSciNet): MR957390
Zentralblatt MATH: 0646.03039
R. Downey and J. Remmel, Classification of degree classes associated with r.e. subspaces, Annals of Pure and Applied Logic, vol. 42 (1989), pp. 105–124.
Mathematical Reviews (MathSciNet): MR996503
Zentralblatt MATH: 0628.03033
Digital Object Identifier: doi:10.1016/0168-0072(89)90051-1
R. Friedberg, A criterion for completeness of degrees of unsolvability, Journal of Symbolic Logic, vol. 22 (1958), pp. 159–160.
Mathematical Reviews (MathSciNet): MR98025
Zentralblatt MATH: 0078.00602
Digital Object Identifier: doi:10.2307/2964177
J. Mohrherr, Density of a final segment of the truth-table degrees, Pacific Journal of Mathematics, vol. 115 (1984), pp. 409–419.
Mathematical Reviews (MathSciNet): MR765197
Zentralblatt MATH: 0534.03018
Project Euclid: euclid.pjm/1102708258
E. Post, Recursively enumerable sets of positive integers and their decision problems, Bulletin of the American Mathematical Society, vol. 50 (1944), pp. 284–316.
Mathematical Reviews (MathSciNet): MR10514
Zentralblatt MATH: 0063.06328
Digital Object Identifier: doi:10.1090/S0002-9904-1944-08111-1
Project Euclid: euclid.bams/1183505800
J. Reimann and T. Slaman, Measures and their random reals, preprint, 2008.
––––, Probability measures and effective randomness, preprint, 2008.
R. Robinson, Jump restricted interpolation in the recursively enumerable degrees, Annals of Mathematics, vol. 93 (1971), no. 2, pp. 586–596.
Mathematical Reviews (MathSciNet): MR313037
Zentralblatt MATH: 0259.02034
Digital Object Identifier: doi:10.2307/1970889
G. Sacks, Recursive enumerability and the jump operator, 1963, vol. 108.
Mathematical Reviews (MathSciNet): MR155747
Zentralblatt MATH: 0118.25103
Digital Object Identifier: doi:10.1090/S0002-9947-1963-0155747-3
J. Shoenfield, On degrees of unsolvability, Annals of Mathematics, vol. 69 (1959), pp. 644–653.
Mathematical Reviews (MathSciNet): MR105355
Zentralblatt MATH: 0119.25105
Digital Object Identifier: doi:10.2307/1970028
R. Soare, Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag, 1987.
Mathematical Reviews (MathSciNet): MR882921
