✦ LIBER ✦

Analytic colorings

✍ Scribed by Wiesław Kubiś; Saharon Shelah

Publisher: Elsevier Science
Year: 2003
Tongue: English
Weight: 194 KB
Volume: 121
Category: Article
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(02)00110-0

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✦ Synopsis

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 deÿne 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 -compact colorings of any prescribed rank ¡ !1. These colorings consistently contain homogeneous sets of cardinality ℵ 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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