On recursive trees with a unique infinite branch
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- by Peter Clote PDF
- Proc. Amer. Math. Soc. 93 (1985), 335-342 Request permission
Abstract:
In this paper we analyze the Turing degree of an infinite branch in a recursive tree $T \subseteq {\omega ^{ < \omega }}$ and its relation to the well-founded part of the tree. It is, of course, not surprising that the two notions are related, but it is of a certain technical interest (in terms of the coding procedure used) to establish the exact interrelation. An interpretation of our result in terms of a Cantor-Bendixson derivative operation on trees $T \subseteq {\omega ^{ < \omega }}$ is given.References
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- C. G. Jockusch Jr. and T. G. McLaughlin, Countable retracing functions and $\Pi _{2}{}^{0}$ predicates, Pacific J. Math. 30 (1969), 67–93. MR 269508
- Hartley Rogers Jr., Theory of recursive functions and effective computability, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1967. MR 0224462
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 93 (1985), 335-342
- MSC: Primary 03D30; Secondary 03D55
- DOI: https://doi.org/10.1090/S0002-9939-1985-0770549-2
- MathSciNet review: 770549