Hyperimmune-free degrees and Schnorr triviality
Johanna N. Y. Franklin
Source: J. Symbolic Logic Volume 73, Issue 3
(2008), 999-1008.
Abstract
We investigate the relationship between lowness for Schnorr randomness and Schnorr triviality. We show that a real is low for Schnorr randomness if and only if it is Schnorr trivial and hyperimmune free.
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Permanent link to this document: http://projecteuclid.org/euclid.jsl/1230396761
Digital Object Identifier: doi:10.2178/jsl/1230396761
Mathematical Reviews number (MathSciNet): MR2444282
Zentralblatt MATH identifier: 05531012
References
Gregory J. Chaitin, A theory of program size formally identical to information theory, Journal of the Association for Computing Machinery, vol. 22 (1975), pp. 329--340.
Mathematical Reviews (MathSciNet): MR411829
Digital Object Identifier: doi:10.1145/321892.321894
Osvald 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
Rod Downey, Evan Griffiths, and Geoffrey Laforte, On Schnorr and computable randomness, martingales, and machines, Mathematical Logic Quarterly, vol. 50 (2004), no. 6, pp. 613--627.
Mathematical Reviews (MathSciNet): MR2096175
Digital Object Identifier: doi:10.1002/malq.200310121
Zentralblatt MATH: 1062.68064
Rod Downey, Denis R. Hirschfeldt, André Nies, and Sebastiaan A. Terwijn, Calibrating randomness, Bulletin of Symbolic Logic, vol. 12 (2006), no. 3, pp. 411--491.
Mathematical Reviews (MathSciNet): MR2248591
Digital Object Identifier: doi:10.2178/bsl/1154698741
Project Euclid: euclid.bsl/1154698741
Zentralblatt MATH: 1113.03037
Rodney G. Downey and Evan J. Griffiths, Schnorr randomness, Journal of Symbolic Logic, vol. 69 (2004), no. 2, pp. 533--554.
Mathematical Reviews (MathSciNet): MR2058188
Digital Object Identifier: doi:10.2178/jsl/1082418542
Project Euclid: euclid.jsl/1082418542
Zentralblatt MATH: 1072.03025
Johanna N. Y. Franklin, Schnorr trivial reals: A construction, Archive for Mathematical Logic, vol. 46 (2008), no. 7--8, pp. 665--678.
Mathematical Reviews (MathSciNet): MR2395564
Digital Object Identifier: doi:10.1007/s00153-007-0061-3
Zentralblatt MATH: 1142.03020
Johanna N. Y. Franklin and Frank Stephan, Schnorr trivial sets and truth-table reducibility, submitted.
Carl G. Jockusch, Jr., Relationships between reducibilities, Transactions of the American Mathematical Society, vol. 142 (1969), pp. 229--237.
Mathematical Reviews (MathSciNet): MR245439
Digital Object Identifier: doi:10.2307/1995354
Zentralblatt MATH: 0188.02604
Bjørn Kjos-Hanssen, André Nies, and Frank Stephan, Lowness for the class of Schnorr random reals, SIAM Journal on Computing, vol. 35 (2005), no. 3, pp. 647--657 (electronic).
Mathematical Reviews (MathSciNet): MR2201451
Digital Object Identifier: doi:10.1137/S0097539704446323
Zentralblatt MATH: 1095.68043
Joseph S. Miller and André Nies, Randomness and computability: Open questions, Bulletin of Symbolic Logic, vol. 12 (2006), no. 3, pp. 390--410.
Mathematical Reviews (MathSciNet): MR2248590
Digital Object Identifier: doi:10.2178/bsl/1154698740
Project Euclid: euclid.bsl/1154698740
Zentralblatt MATH: 1169.03033
André Nies, Lowness properties and randomness, Advances in Mathematics, vol. 197 (2005), no. 1, pp. 274--305.
Mathematical Reviews (MathSciNet): MR2166184
Digital Object Identifier: doi:10.1016/j.aim.2004.10.006
Zentralblatt MATH: 1141.03017
André Nies, Frank Stephan, and Sebastiaan A. Terwijn, Randomness, relativization and Turing degrees, Journal of Symbolic Logic, vol. 70 (2005), no. 2, pp. 515--535.
Mathematical Reviews (MathSciNet): MR2140044
Digital Object Identifier: doi:10.2178/jsl/1120224726
Project Euclid: euclid.jsl/1120224726
Zentralblatt MATH: 1090.03013
C.-P. Schnorr, A unified approach to the definition of random sequences, Mathematical Systems Theory. An International Journal on Mathematical Computing Theory, vol. 5 (1971), pp. 246--258.
Mathematical Reviews (MathSciNet): MR354328
Digital Object Identifier: doi:10.1007/BF01694181
Zentralblatt MATH: 0227.62005
Robert I. Soare, Recursively enumerable sets and degrees, Perspectives in Mathematical Logic, Springer-Verlag, 1987.
Mathematical Reviews (MathSciNet): MR882921
Sebastiaan A. Terwijn and Domenico Zambella, Computational randomness and lowness, Journal of Symbolic Logic, vol. 66 (2001), no. 3, pp. 1199--1205.
Mathematical Reviews (MathSciNet): MR1856736
Digital Object Identifier: doi:10.2307/2695101
JSTOR: links.jstor.org
Zentralblatt MATH: 0990.03033