Analytic Colorings
Logic
2007-05-23 v1
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.
Cite
@article{arxiv.math/0212026,
title = {Analytic Colorings},
author = {Wieslaw Kubís and Saharon Shelah},
journal= {arXiv preprint arXiv:math/0212026},
year = {2007}
}