Analytic Colorings

Wieslaw Kubís; Saharon Shelah

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Analytic Colorings

Wieslaw Kubís·Saharon Shelah

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Abstract

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<omega_1. These colorings consistently contain homogeneous sets of cardinality aleph_gamma but they do not contain perfect homogeneous sets. As an application, we discuss the so-called defectedness coloring of subsets of Polish linear spaces.

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BibTeX RIS

Wieslaw Kubís, Saharon Shelah. 2002-12-02. Analytic Colorings. https://arxiv.org/abs/math/0212026

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