A high dimensional Open Coloring Axiom

✍ Scribed by Bin He

• Book ID: 102484100
• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 141 KB
• Volume: 51
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.200510003

✦ Synopsis

Abstract

We prove a partition theorem for analytic sets, namely, if X is an analytic set in a Polish space and [X]^n^ = K~0~ ∪ K~1~ with K~0~ open in the relative topology, and the partition satisfies a finitary condition, then either there is a perfect K~0~‐homogeneous subset or X is a countable union of K~1~‐homogeneous subsets. We also prove a partition theorem for analytic sets in the three‐dimensional case. Finally, we give some applications of the theorems. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)