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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On recursive trees with a unique infinite branch

Author: Peter Clote
Journal: Proc. Amer. Math. Soc. 93 (1985), 335-342
MSC: Primary 03D30; Secondary 03D55
MathSciNet review: 770549
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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.

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Keywords: Hyperarithmetic, well-founded part of a tree, Cantor-Bendixson rank
Article copyright: © Copyright 1985 American Mathematical Society

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