Algebraic Model Theory

Recent major advances in model theory include connections between model theory and Diophantine and real analytic geometry, permutation groups, and finite algebras. The present book contains lectures on recent results in algebraic model theory, covering topics from the following areas: geometric model theory, the model theory of analytic structures, permutation groups in model theory, the spectra of countable theories, and the structure of finite algebras. Audience: Graduate students in logic and others wishing to keep abreast of current trends in model theory. The lectures contain sufficient introductory material to be able to grasp the recent results presented.

Inhalt

Preface. An Introduction to Independence and Local Modularity; E. Bouscaren. Groups Definable in ACFA; Z. Chatzidakis. Large Finite Structures with Few Types; G. Cherlin. A Survey of the Uncountable Spectra of Countable Theories; B. Hart, M.C. Laskowski. An Introduction to Tame Congruence Theory; E.W. Kiss. Stable Finitely Homogeneous Structures: A Survey; A.H. Lachlan. Homogeneous and Smoothly Approximated Structures; D. Macpherson. Khovanskii's Theorem; D. Marker. ACFA and the Manin-Mumford Conjecture; A. Pillay. Decidable Equational Classes; M.A. Valeriote. Schanuel's Conjecture and the Decidability of the Real Exponential Field; A.J. Wilkie. Three Lectures on the RS Problem; R. Willard. Decidable Modules; M. Ziegler. Index.