The first volume in this set aims 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 Lindstrom, presents the early history of the concept of generalized quantifier. The volume then continues with a series of papers surveying various research areas, particularly those that are of current interest. Together these papers provide introductions to the subject from the points of view of mathematics, linguistics, and theoretical computer science. The second volume contains a collection of research papers on the subject in new areas. The two volumes are complementary.
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Preface. Quantifiers and Inference; J. van Benthem. Operators on Branched Quantifiers; M.A. Brown. Hilbert's Epsilon-Symbol in the Presence of Generalized Quantifiers; X. Caicedo. Partially Ordered Connectives and Finite Graphs; L. Hella, G. Sandu. Theories of Finitely Determined Linear Orderings in Stationary Logics; H. Herre. Definable Second-Order Quantifiers and Quasivarieties; A.A. Ivanov. Quantifiers Determined by Classes of Binary Relations; M. Krynicki. Decidability Results for Classes of Ordered Abelian Groups in Logics with Ramsey Quantifiers; W. Lenski. On the Eliminability of the Quantifier `There Exists Uncountably Many'; Z. Mijajlovic. Quantifiers Definable by Second Order Means; M. Mostowski. Generalized Quantifiers in Algebra; A.G. Pinus. On Ordering of the Family of Logics with Skolem-Löwenheim Property and Countable Compactness Property; M. Waclawek.DAGGER. Pre-Ordered Quantifiers in Elementary Sentences of Natural Language; M.W. Zawadowsky. Some Remarks on Zawadowski's `Theory of Preordered Quantifiers'; M.A. Brown. Index of Names.
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