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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
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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.

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S. B. Cooper, Computability theory, Chapman & Hall, CRC Press, Boca Raton, FL, New York, London (2004). MR 2017461 (2005h:03001)

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T. Slaman and M. Groszek, A basis theorem for perfect sets, Bulletin of Symbolic Logic, volume 4, number 2 (1998). MR 1632148 (99c:03072)

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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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