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On degree-preserving homeomorphisms between trees in computable topology

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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 2ω. 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′.

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Authors and Affiliations

  1. Department of Mathematics, Western Illinois University, Macomb, IL, 61455, USA

    Iraj Kalantari & Larry Welch

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  1. Iraj Kalantari
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  2. Larry Welch
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Correspondence to Iraj Kalantari.

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Kalantari, I., Welch, L. On degree-preserving homeomorphisms between trees in computable topology. Arch. Math. Logic 46, 679–693 (2008). https://doi.org/10.1007/s00153-007-0056-0

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  • DOI: https://doi.org/10.1007/s00153-007-0056-0

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