Journal of Symbolic Logic 66 (1):56-86 (2001)
| Abstract |
We consider Borel sets of finite rank $A \subseteq\Lambda^\omega$ where cardinality of Λ is less than some uncountable regular cardinal K. We obtain a "normal form" of A, by finding a Borel set Ω, such that A and Ω continuously reduce to each other. In more technical terms: we define simple Borel operations which are homomorphic to ordinal sum, to multiplication by a countable ordinal, and to ordinal exponentiation of base K, under the map which sends every Borel set A of finite rank to its Wadge degree
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| DOI | 10.2307/2694911 |
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Inside the Muchnik Degrees I: Discontinuity, Learnability and Constructivism.K. Higuchi & T. Kihara - 2014 - Annals of Pure and Applied Logic 165 (5):1058-1114.
Classical and Effective Descriptive Complexities of Ω-Powers.Olivier Finkel & Dominique Lecomte - 2009 - Annals of Pure and Applied Logic 160 (2):163-191.
Topological Complexity of Locally Finite Ω-Languages.Olivier Finkel - 2008 - Archive for Mathematical Logic 47 (6):625-651.
Inside the Muchnik Degrees II: The Degree Structures Induced by the Arithmetical Hierarchy of Countably Continuous Functions.K. Higuchi & T. Kihara - 2014 - Annals of Pure and Applied Logic 165 (6):1201-1241.
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