Analytic Colorings
| dc.creator | Kubís, Wieslaw | |
| dc.creator | Shelah, Saharon | |
| dc.date | 2002-12-02 | |
| dc.date.accessioned | 2026-07-07T04:53:28Z | |
| dc.date.available | 2026-07-07T04:53:28Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/math/0212026 | |
| dc.identifier | http://arxiv.org/abs/math/0212026 | |
| dc.identifier | Ann. Pure Appl. Logic 121 No. 2-3 (2003) 145--161 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65861 | |
| dc.subject | Logic | |
| dc.title | Analytic Colorings | |
| dc.type | text |