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Stable Groups
In this book the general theory of stable groups is developed from the beginning.
Simplicity Theory
An up-to-date account of the current techniques and results in Simplicity Theory, which has been a focus of research in model theory for the last decade. Suitable for logicians, mathematicians and graduate students working on model theory.
Mathematical Logic in the 20th Century
This invaluable book is a collection of 31 important both inideas and results papers published by mathematical logicians inthe 20th Century. The papers have been selected by Professor Gerald ESacks. Some of the authors are Gdel, Kleene, Tarski, A Robinson, Kreisel, Cohen, Morley, Shelah, Hrushovski and Woodin.
The Notre Dame Lectures
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. In the fall of 2000, the logic community at the University of Notre Dame, Indiana hosted Greg Hjorth, Rodney G. Downey, Zoé Chatzidakis and Paola D'Aquino as visiting lecturers. Each of them presented a month-long series of expository lectures at the graduate level. This volume, the eighteenth publication in the Lecture Notes in Logic series, contains refined and expanded versions of those lectures. The four articles are entitled 'Countable models and the theory of Borel equivalence relations', 'Model theory of difference fields', 'Some computability-theoretic aspects of reals and randomness' and 'Weak fragments of Peano arithmetic'.
A Course in Model Theory
Concise introduction to current topics in model theory, including simple and stable theories.
A Guide to Classical and Modern Model Theory
This volume is easily accessible to young people and mathematicians unfamiliar with logic. It gives a terse historical picture of Model Theory and introduces the latest developments in the area. It further provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. The book is for trainees and professional model theorists, and mathematicians working in Algebra and Geometry.
Model Theory and Algebraic Geometry
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry: Volume 2
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.
Finite Structures with Few Types
This book applies model theoretic methods to the study of certain finite permutation groups, the automorphism groups of structures for a fixed finite language with a bounded number of orbits on 4-tuples. Primitive permutation groups of this type have been classified by Kantor, Liebeck, and Macpherson, using the classification of the finite simple groups. Building on this work, Gregory Cherlin and Ehud Hrushovski here treat the general case by developing analogs of the model theoretic methods of geometric stability theory. The work lies at the juncture of permutation group theory, model theory, classical geometries, and combinatorics. The principal results are finite theorems, an associated a...
A Guide to NIP Theories
The first book to introduce the rapidly developing subject of NIP theories, for students and researchers in model theory.
