Model theory : an introduction
"This book is a modern introduction to model theory that stresses applications to algebra throughout the text. The first half of the book includes classical material on model construction techniques, type spaces, prime models, saturated models, countable models, and indiscernibles and their applications. The author also includes an introduction to stability theory beginning with Morley's Categoricity Theorem and concentrating on omega-stable theories. One significant aspect of this text is the inclusion of chapters on important topics not covered in other introductory texts, such as omega-stable groups and the geometry of strongly minimal sets. The author then goes on to illustrate how these ingredients are used in Hrushovski's applications to diophantine geometry."--Jacket
viii, 342 pages ; 25 cm.
9780387987606, 9786610010615, 9780387227344, 0387987606, 6610010617, 0387227342
49326991
Printed edition
Structures and theories : Languages and structures ; Theories ; Definable sets and interpretability
Basic techniques : The compactness theorem ; Complete theories ; Up and down ; Back and forth
Algebraic examples : Quantifier elimination ; Algebraically closed fields ; Real closed fields
Realizing and omitting types : Types ; Omitting types and prime models ; Saturated and homogeneous models ; The number of countable models
Indiscernibles : Partition theorems ; Order indiscernibles ; A many-models theorem ; An independence result in arithmetic
w-Stable theories : Uncountably categorical theories ; Morley rank ; Forking and independence ; Uniqueness of prime model extensions ; Morley sequences
w-Stable groups : The descending chain condition ; Generic types ; The indecomposability theorem ; Definable groups in algebraically closed fields ; Finding a group
Geometry of strongly minimal sets : Pregeometries ; Canonical bases and families of plane curves ; Geometry and algebra
English
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