A blend of methods of recursion theory and topology: A Π1 0 tree of shadow points [Book Review]

Archive for Mathematical Logic 43 (8):991-1008 (2004)
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Abstract

This paper is a sequel to our [7]. In that paper we constructed a Π1 0 tree of avoidable points. Here we construct a Π1 0 tree of shadow points. This tree is a tree of sharp filters, where a sharp filter is a nested sequence of basic open sets converging to a point. In the construction we assign to each basic open set on the tree an address in 2<ω. One interesting fact is that while our Π1 0 tree of sharp filters (a subtree of Δ<ω) is isomorphic to the tree of addresses (a subtree of 2<ω), the tree of addresses is recursively enumerable but not recursive. To achieve this end we use a finite injury priority argument

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References found in this work

$\pi^0_1$-classes And Rado's Selection Principle.C. G. Jockusch, A. Lewis & J. B. Remmel - 1991 - Journal of Symbolic Logic 56 (2):684-693.
A blend of methods of recursion theory and topology.Iraj Kalantari & Larry Welch - 2003 - Annals of Pure and Applied Logic 124 (1-3):141-178.
Π01-classes and Rado's selection principle.C. G. Jockusch, A. Lewis & J. B. Remmel - 1991 - Journal of Symbolic Logic 56 (2):684 - 693.

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