Quantifiers: Logics, Models and Computation is the first concentrated effort to give a systematic presentation of the main research results on the subject, since the modern concept was formulated in the late '50s and early '60s. The majority of the papers are in the nature of a handbook. All of them are self-contained, at various levels of difficulty. The Introduction surveys the main ideas and problems encountered in the logical investigation of quantifiers. The Prologue, written by Per Lindström, presents the early history of the concept of generalised quantifiers. The volume then continues with a series of papers surveying various research areas, particularly those that are of current interest. Together they provide introductions to the subject from the points of view of mathematics, linguistics, and theoretical computer science. The present volume has been prepared in parallel with Quantifiers: Logics, Models and Computation, Volume Two. Contributions, which contains a collection of research papers on the subject in areas that are too fresh to be summarised. The two volumes are complementary. For logicians, mathematicians, philosophers, linguists and computer scientists. Suitable as a text for advanced undergraduate and graduate specialised courses in logic.

Inhalt

Preface. Quantifiers, Some Problems and Ideas; M. Krynicki, M. Mostowski. Prologue; P. Lindström. On the Model Theory of Some Generalized Quantifiers; H.D. Ebbinghaus. Finite Generation Problem and n-ary Quantifiers; L. Hella, K. Luosto. Games and Trees in Infinitary Logic: a Survey; J. Väänäen. Theory of Linear Order in Extended Logics; H. Herre. Henkin Quantifiers; M. Krynicki, M. Mostowski. Continuous Operations on Spaces of Structures; X. Caicedo. Model Theory of Topological Structures; J. Flum. Computable Quantifiers and Logics over Finite Structures; J.A. Makowski, Y.B. Pnueli. Quantifiers in Natural Language. A Survey of Some Recent Work; D. Westerståhl. Index of Names.