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ISSN 1088-6826(e) ISSN 0002-9939(p)

There are $2^{\aleph_{0}}$ many -degrees in the random reals

Author(s): Liang Yu; Decheng Ding
Journal: Proc. Amer. Math. Soc. 132 (2004), 2461-2464.
MSC (2000): Primary 03D25
Posted: March 25, 2004
MathSciNet review: 2052426
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Abstract | References | Similar articles | Additional information

Abstract: We prove that there are $2^{\aleph_{0}}$ many -degrees in the random reals.

References:

1.: Rodney G. Downey and Denis Hirschfeldt. Algorithmic Randomness and Complexity, in preparation.
2.: Rodney Downey, Denis Hirschfeldt, and André Nies, Randomness, computability and density, SIAM Journal of Computing 31 (2002), 1169-1183. MR 2003f:03057
3.: Rodney G. Downey, Denis R. Hirschfeldt, André Nies and Frank Stephan, Trivial reals. Electronic Notes in Theoretical Computer Science (ENTCS), 2002.
4.: Rod Downey and Guohua Wu, personal communication.
5.: Antonin Kucera and Theodore A. Slaman, Randomness and recursive enumerability, SIAM J. Comput. 31 (2001), 199-211. MR 2002k:68078
6.: Yiannis N. Moschovakis, Desciptive Set Theory, North-Holland, Amsterdam, 1980. MR 82e:03002
7.: Robert M. Solovay, Draft of paper (or series of papers) on Chaitin's work, unpublished notes, May, 1975, 215 pages.
8.: Liang Yu, Decheng Ding, and Rod Downey. The complexity of the random reals, submitted.

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Additional Information:

Liang Yu
Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiang Su, China
Email: yuliang@mcs.vuwa.ac.nz

Decheng Ding
Affiliation: Department of Mathematics, Nanjing University, Nanjing, Jiang Su, China
Email: dcding@nju.edu.cn

DOI: 10.1090/S0002-9939-04-07417-9
PII: S 0002-9939(04)07417-9
Received by editor(s): April 17, 2003
Received by editor(s) in revised form: May 28, 2003
Posted: March 25, 2004
Additional Notes: We thank Professor Rodney Downey for his nice comments. Both of the authors are supported by NSF of China No.19931020, 60310213 and the Ph.D. project of the State Education Ministry of China. The first author is also supported by a postdoctoral fellowship of the New Zealand Institute for Mathematics and its Applications, Centre of Research Excellence.
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 2004, American Mathematical Society

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