THE NORMAL-FORM OF BOREL SETS .1. BOREL SETS OF FINITE RANK

For each Borel set of reals A, of finite rank, we obtain a ''normal'' form of A, by finding a Borel set Omega of maximum simplicity, such th at A and Omega continuously reduce to each other. In more technical te rms: we defined simple Borel operations which are homomorphic to ordin al sum, to multiplication by a countable ordinal, and to ordinal expon entiation of base omega(1), under the map which sends every Borel set A of finite rank to its Wadge degree.