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Wadge hierarchy and Veblen hierarchy Part I: Borel sets of finite rank

Published online by Cambridge University Press:  12 March 2014

J. Duparc
J. Duparc*
Affiliation:
Equipe de Logique Mathématique, CNRS URA 753, et Université Paris VII, U.F.R. de Mathématiques, 2 Place Jussieu. 75251 Paris Cedex 05, France, E-mail: [email protected]
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Abstract

We consider Borel sets of finite rank A ⊆ ∧ω where cardinality of Λ is less than some uncountable regular cardinal . 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 , under the map which sends every Borel set A of finite rank to its Wadge degree.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 1 , March 2001 , pp. 56 - 86
Copyright
Copyright © Association for Symbolic Logic 2001

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References

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