On degree-preserving homeomorphisms between trees in computable topology

Archive for Mathematical Logic 46 (7-8):679-693 (2008)

Abstract
In this paper we first give a variant of a theorem of Jockusch–Lewis– Remmel on existence of a computable, degree-preserving homeomorphism between a bounded strong ${\Pi^0_2}$ class and a bounded ${\Pi^0_1}$ class in 2 ω . Namely, we show that for mathematically common and interesting topological spaces, such as computably presented ${\mathbb{R}^n}$ , we can obtain a similar result where the homeomorphism is in fact the identity mapping. Second, we apply this finding to give a new, priority-free proof of existence of a tree of shadow points computable in 0′
Keywords Computability theory  Recursion theory  Topology  Recursive analysis  Computable analysis  Recursive topology  Computable topology  Avoidable points  Shadow points
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DOI 10.1007/s00153-007-0056-0
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References found in this work BETA

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.
$\Pi^0_1$-Classes And Rado's Selection Principle.C. G. Jockusch, A. Lewis & J. B. Remmel - 1991 - Journal of Symbolic Logic 56 (2):684-693.

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