# Sh:802

- Kubiś, W., & Shelah, S. (2003).
*Analytic colorings*. Ann. Pure Appl. Logic,**121**(2-3), 145–161. arXiv: math/0212026 DOI: 10.1016/S0168-0072(02)00110-0 MR: 1982945 -
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. - 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}, doi = {10.1016/S0168-0072(02)00110-0}, mrclass = {03E05 (03E15 03E35 54H05)}, mrnumber = {1982945}, mrreviewer = {Otmar Spinas}, doi = {10.1016/S0168-0072(02)00110-0}, note = {\href{https://arxiv.org/abs/math/0212026}{arXiv: math/0212026}}, arxiv_number = {math/0212026} }