This material, presented at the famous Cabal seminar, appeared in four volumes of Springer Lecture Notes in Mathematics over the years 1978-1988. For those interested in set theory with the axiom of determinacy instead of the axiom of choice, it was the ultimate source of knowledge for decades. Now, edited by A. S. Kechris, B. Löwe and J. R. Steel, the Cabal seminar appears once more in a beautifully typed book, which is quite different from a mere reprint of the previous Lecture Notes. Instead, the material is carefully organized so that it may serve as an advanced textbook equally well as a monograph on descriptive set theory. The book is divided into two parts; both parts have long informative introductions, written by John R. Steel for 'Games and scales' and by Steve Jackson for 'Suslin cardinals'. Seven papers are new and 12 are reprinted from the previous “Proceedings of Cabal Seminar”.

Reviewer:

psim