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A Normal Form of Borel Sets of Finite Rank
submitted to Notre-Dame Journal of Formal Logic radically different proofs and tools than the ones in the article submitted to JSL. These proofs are close to the ones in my Ph.D. Thesis, but extremely reduced
For each Borel set of reals A, of finite rank, we obtain a ``normal form'' of A, by finding a canonical 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 ω1 , under the map which sends every Borel set A of finite rank to its Wadge degree.
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