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The Normal Form of Borel Sets. Part I: Borel Sets of Finite Rank
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics,
For each Borel set of reals A, of finite rank, we obtain a "normal form" of A, by finding a Borel set Ω of maximum simplicity, 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 ω1, under the map which sends every Borel set A of finite rank to its Wadge degree.
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