Proceedings of the American Mathematical Society

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

On a question of Slaman and Groszek

Author(s): Andrew E. M. Lewis
Journal: Proc. Amer. Math. Soc. 136 (2008), 3663-3668.
MSC (2000): Primary 03D28
Posted: May 16, 2008
MathSciNet review: 2415052
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Abstract | References | Similar articles | Additional information

Abstract: We answer a question of Slaman and Groszek by showing that any non-computable perfect tree computes one of its non-computable paths.

References:

[BC]: S. B. Cooper, Computability theory, Chapman & Hall, CRC Press, Boca Raton, FL, New York, London (2004). MR 2017461 (2005h:03001)
[HF]: H. Friedman, 102 problems in mathematical logic, Journal of Symbolic Logic, volume 40, (1975), pp. 113-129. MR 0369018 (51:5254)
[AL]: A. E. M. Lewis, $\Pi^0_1$ classes, strong minimal covers and hyperimmune-free degrees, Bulletin of the London Mathematical Society, volume 39, number 6 (2007), 892-910.
[AL2]: -, A random degree with strong minimal cover, Bulletin of the London Mathematical Society, volume 39, number 5 (2007), 848-856. MR 2365234
[AL3]: -, Strong minimal covers and a question of Yates: the story so far, to appear in the proceedings of the ASL meeting 2006.
[SG]: T. Slaman and M. Groszek, A basis theorem for perfect sets, Bulletin of Symbolic Logic, volume 4, number 2 (1998). MR 1632148 (99c:03072)
[RS]: R. I. Soare, Recursively enumerable sets and degrees, Springer, New York (1987). MR 882921 (88m:03003)

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Additional Information:

Andrew E. M. Lewis
Affiliation: Department of Mathematics, University of Leeds, Leeds, LS2 9JT England
Email: andy@aemlewis.co.uk

DOI: 10.1090/S0002-9939-08-09345-3
PII: S 0002-9939(08)09345-3
Received by editor(s): April 24, 2007,
Received by editor(s) in revised form: August 31, 2007, and September~4, 2007
Posted: May 16, 2008
Additional Notes: The author was supported by the Marie-Curie Fellowship MEIF-CT-2005-023657 and partially supported by the NSFC Grand International Joint Project no. 60310213, New Directions in the Theory and Applications of Models of Computation.
Communicated by: Julia Knight
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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