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The computable dimension of trees of infinite height

Published online by Cambridge University Press:  12 March 2014

Russell Miller
Russell Miller*
Affiliation:
Department of Mathematics, Queens College, – C.U.N.Y., 65-30 Kissena Blvd., Flushing, New York 11367, USA, E-mail: [email protected]
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Abstract

We prove that no computable tree of infinite height is computably categorical, and indeed that all such trees have computable dimension ω. Moreover, this dimension is effectively ω, in the sense that given any effective listing of computable presentations of the same tree, we can effectively find another computable presentation of it which is not computably isomorphic to any of the presentations on the list.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 1 , March 2005 , pp. 111 - 141
Copyright
Copyright © Association for Symbolic Logic 2005

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