Model-Theoretic Logics

This book brings together several directions of work in model theory between the late 1950s and early 1980s.

J. Barwise (Edited by), S. Feferman (Edited by)

9781107168251, Cambridge University Press

Hardback, published 2 March 2017

911 pages, 11 b/w illus.
24 x 16.3 x 5.8 cm, 1.58 kg

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. L?1? 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.

Subject Areas: Topology [PBP], Calculus & mathematical analysis [PBK], Set theory [PBCH], Mathematical logic [PBCD]