Ebook: 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.

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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.

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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.
Content:
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

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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.
Content:
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
....