Analysis and Logic

Rating:
Summary: A very good book
Review: The book is a technically demanding volume containing three articles at the frontier of mathematical logic and modern analysis. All articles apply set theoretical techniques to problems arising from modern Analysis. The first is a study of model theory of Banach spaces by C. Ward Henson and Jose Iovino, the second on actions of Polish groups and Classification problems by A.S.Kechris, and the third by E.Odell on distortion of Banach spaces.

The part written by A.S. Kechris, one of the leading researchers in descriptive set theory, is basically a survey of recent developments in the theory of Borel equivalence relations. This theory has been applied to classification problems in several areas of mathematics, and its proof techniques rely on descriptive set theory. The article also presents many relevant examples of group actions etc. The recently discovered theory of turbulence is treated thoroughly. I like the elucidating style and would recommend this survey to anyone with interest in this area.