# Sh:802

• Kubiś, W., & Shelah, S. (2003). Analytic colorings. Ann. Pure Appl. Logic, 121(2-3), 145–161.
• 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.
• Current version: 2002-08-09_10 (15p) published version (17p)
Bib entry
@article{Sh:802,
author = {Kubi{\'s}, Wies{\l}aw and Shelah, Saharon},
title = {{Analytic colorings}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {121},
number = {2-3},
year = {2003},
pages = {145--161},
issn = {0168-0072},
mrnumber = {1982945},
mrclass = {03E05 (03E15 03E35 54H05)},
doi = {10.1016/S0168-0072(02)00110-0},
note = {\href{https://arxiv.org/abs/math/0212026}{arXiv: math/0212026}},
arxiv_number = {math/0212026}
}