Model Theory [Hardcover]

Formal logic, free from the ambiguities of natural languages, is especially suited for use in computing. In turn, model theory, which is concerned with the relationship between mathematical structures and logic, now has a wide range of applications in areas such as computing, philosophy, and linguistics. Model theory's power comes from its usefulness in defining new structures and in classifying existing ones by establishing links between them. This book, suitable for both mathematicians and students from outside the field, provides a clear and readable introduction to the subject. It includes brief historically background for each major topic and consistently points out the motivations for each new development. The proofs are also explained in detail.

1. Basic notions: universal algebra
2. First order languages: semantics
3. Completeness of first order logic
4. Basic notions: model theory
5. The compactness theorem
6. L?wenheim-Skolem theorems
7. Complete and categorical theories

This is an excellent pedagogically oriented introductory text on classical model theory addressed to students without any previous background in logic. It seems suitable for advanced undergraduate mathematics majors, and might equally be used as a motivated (and motivating) introduction to mathematical logic. The large number of examples, exercises and problems placed at the end of each section will well serve the learner, be it in a course or in self-study. The preface by J. Mosterin furnishes a valuable perspective of the scope and development of model theory. The detailed glossary of symbols and abbreviations coupled with a good index enhances the use of this text. . . . All in all, this is a carefully written book based on considerable experience in teaching model theory and thus is highly suitable for adoption as a classroom text. --Mathematical Reviews

[C]onsider odel Theory by Manzano. This book is especially well written. Each cl£&