Constructibility

This book is intended to give a fairly comprehensive account of the theory of constructible sets at an advanced level. The intended reader is a graduate mathe matician with some knowledge of mathematical logic. In particular, we assume familiarity with the notions of formal languages, axiomatic theories in formal languages, logical deductions in such theories, and the interpretation oflanguages in structures. Practically any introductory text on mathematical logic will supply the necessary material. We also assume some familiarity with Zermelo-Fraenkel set theory up to the development or ordinal and cardinal numbers. Any number of texts would suffice here, for instance Devlin (1979) or Levy (1979). The book is not intended to provide a complete coverage of the many and diverse applications of the methods of constructibility theory, rather the theory itself. Such applications as are given are there to motivate and to exemplify the theory. The book is divided into two parts. Part A ("Elementary Theory") deals with the classical definition of the La-hierarchy of constructible sets. With some prun ing, this part could be used as the basis of a graduate course on constructibility theory. Part B ("Advanced Theory") deals with the fa-hierarchy and the Jensen "fine-structure theory".