Hailed by the Bulletin of the American Mathematical Society as "easy to use and a pleasure to read," this research monograph is recommended for students and professionals interested in model theory and definability theory. The sole prerequisite is a familiarity with the basics of logic, model theory, and set theory. 1974 edition.

The revised edition contains a new chapter which provides an elegant description of the semantics. The various classes of lambda calculus models are described in a uniform manner. Some didactical improvements have been made to this edition. An example of a simple model is given and then the general theory (of categorical models) is developed. Indications are given of those parts of the book which can be used to form a coherent course.