Algebraic model theory : [papers from the NATO Advanced Study Institute on "Algebraic Model Theory", 1996, Fields Institute, Toronto, Ont

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. Front Matter....Pages i-xvii An Introduction to Independence and Local Modularity....Pages 1-24 Groups Definable in ACFA....Pages 25-52 Large Finite Structures with Few Types....Pages 53-105 A Survey of the Uncountable Spectra of Countable Theories....Pages 107-118 An Introduction to Tame Congruence Theory....Pages 119-143 Stable Finitely Homogeneous Structures: A Survey....Pages 145-159 Homogeneous and Smoothly Approximated Structures....Pages 161-179 Khovanskii’s Theorem....Pages 181-193 ACFA and the Manin-Mumford Conjecture....Pages 195-205 Decidable Equational Classes....Pages 207-221 Schanuel’s Conjecture and the Decidability of the Real Exponential Field....Pages 223-230 Three Lectures on the RS Problem....Pages 231-254 Decidable Modules....Pages 255-274 Back Matter....Pages 275-277

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.

Proceedings of the NATO Advanced Study Institute on Algebraic Model Theory, Toronto, Canada, 19-30 August 1996