Model-Theoretic Logics Perspectives in Logic Series

Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the eighth publication in the Perspectives in Logic series, brings together several directions of work in model theory between the late 1950s and early 1980s. It contains expository papers by pre-eminent researchers. Part I provides an introduction to the subject as a whole, as well as to the basic theory and examples. The rest of the book addresses finitary languages with additional quantifiers, infinitary languages, second-order logic, logics of topology and analysis, and advanced topics in abstract model theory. Many chapters can be read independently.

List of contributors; Part I. Introduction, Basic Theory and Examples: 1. Model-theoretic logics: background and aims J. Barwise; 2. Extended logics: the general framework H.-D. Ebbinghaus; 3. Characterizing logics J. Flum; Part II. Finitary Languages with Additional Quantifiers: 4. The quantifier 'there exist uncountably many' and some of its relatives M. Kaufmann; 5. Transfer theorems and their applications to logics J. H. Schmerl; 6. Other quantifiers: an overview D. Mundici; 7. Decidability and quantifier-elimination A. Baudisch, D. Seese, P. Tuschik and M. Weese; Part III. Infinitary Languages: 8. Lω1ω and admissible fragments M. Nadel; 9. Larger infinitary languages M. A. Dickmann; 10. Game quantification Ph. G. Kolaitis; 11. Applications to algebra P. C. Ecklof; Part IV. Second-Order Logic: 12. Definable second-order quantifiers J. Baldwin; 13. Monadic second-order theories Y. Gurevich; Part V. Logics of Topology and Analysis: 14. Probability quantifiers H. J. Keisler; 15. Topological model theory M. Ziegler; 16. Borel structures and measure and category logics C. I. Steinhorn; Part VI. Advanced Topics in Abstract Model Theory: 17. Set-theoretic definability of logics J. Väänänen; 18. Compactness, embeddings and definability J. A. Makowsky; 19. Abstract equivalence relations J. A. Makowsky and D. Mundici; 20. Abstract embedding relations J. A. Makowsky; Bibliography D. S. Scott, D. C. McCarthy and J. F. Horty.

J. Barwise works in the Center for the Study of Language and Information at Stanford University, California.
S. Feferman works in the Department of Mathematics and Philosophy at Stanford University, California.