This book contains three large articles, based on minicourses presented by the authors during the conference “Analyse & Logique” at Mons, Belgium, in 1997. These papers are: Ultraproducts in Analysis, by C. W. Henson and I. Jovino, Actions of Polish Groups and Classifications Problems by A. S. Kechris and On Subspaces, Asymptotic Structure, and Distortion of Banach Spaces; Connection with Logic, by E. Odell. In each case, the title neatly describes the contents of the corresponding section. Every paper follows the standard pattern of a conference minicourse: It assumes a very low-level familiarity with the subject, explains basic notions and crucial examples, then takes a short path to quite recent deep theorems. Many times, proofs are omitted; instead, emphasis is given to the meaning of theorems and their interrelations. Each paper has its own extensive bibliography. One does not need to be a specialist in analysis to find this book a worthy item in the library.

Reviewer:

psim