Analytic Colorings

Details Analytic Colorings Analytic Colorings

2002-12-02

arxiv.org/abs/math/0212026v1

Mathematics

Logic

Scientific paper

We investigate the existence of perfect homogeneous sets for analytic colorings. An analytic coloring of X is an analytic subset of [X]^N, where N>1 is a natural number. We define an absolute rank function on trees representing analytic colorings, which gives an upper bound for possible cardinalities of homogeneous sets and which decides whether there exists a perfect homogeneous set. We construct universal sigma-compact colorings of any prescribed rank gamma

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