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Model Theory : An Introduction 2002 ed. [Kõva köide]

  • Formaat: Hardback, 345 pages, kõrgus x laius: 235x155 mm, kaal: 699 g, VIII, 345 p., 1 Hardback
  • Sari: Graduate Texts in Mathematics 217
  • Ilmumisaeg: 21-Aug-2002
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387987606
  • ISBN-13: 9780387987606
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  • Formaat: Hardback, 345 pages, kõrgus x laius: 235x155 mm, kaal: 699 g, VIII, 345 p., 1 Hardback
  • Sari: Graduate Texts in Mathematics 217
  • Ilmumisaeg: 21-Aug-2002
  • Kirjastus: Springer-Verlag New York Inc.
  • ISBN-10: 0387987606
  • ISBN-13: 9780387987606
"Model theory is the branch of mathematical logic that examines what it means for a first-order sentence... to be true in a particular structure....This is a text for graduate students, mainly aimed at those specializing in logic, but also of interest for mathematicians outside logic who want to know what model theory can offer them...it is one which makes a good case for model theory as much more than a tool for specialist logicians." -- THE MATHEMATICAL GAZETTE

Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures

Arvustused

From the reviews:



MATHEMATICAL REVIEWS



"This is an extremely fine graduate level textbook on model theory. There is a careful selection of topicsThere is a strong focus on the meaning of model-theoretic concepts in mathematically interesting examples. The exercises touch on a wealth of beautiful topics."



"This is an extremely fine graduate level textbook on model theory. There is a careful selection of topics, with a route leading to a substantial treatment of Hrushovskis proof of the Mordell-Lang conjecture for function fields. The exercises touch on a wealth of beautiful topics. There is additional basic background in two appendices (on set theory and on real algebra)." (Dugald Macpherson, Mathematical Reviews, 2003 e)



"Model theory is the branch of mathematical logic that examines what it means for a first-order sentence to be true in a particular structure . This is a text for graduate students, mainly aimed at those specializing in logic, but also of interest for mathematicians outside logic who want to know what model theory can offer them in their own disciplines. it is one which makes a good case for model theory as much more than a tool for specialist logicians." (Gerry Leversha, The Mathematical Gazette, Vol. 88 (513), 2004)



"The authors intended audience for this high level introduction to model theory is graduate students contemplating research in model theory, graduate students in logic, and mathematicians who are not logicians but who are in areas where model theory has interesting applications. The text is noteworthy for its wealth of examples and its desire to bring the student to the point where the frontiers of research are visible. this book should be on the shelf of anybody with an interest in model theory." (J. M. Plotkin, Zentralblatt Math, Vol. 1003 (03), 2003)

Introduction 1(6)
Structures and Theories
7(26)
Languages and Structures
7(7)
Theories
14(5)
Definable Sets and Interpretability
19(10)
Exercises and Remarks
29(4)
Basic Techniques
33(38)
The Compactness Theorem
33(7)
Complete Theories
40(4)
Up and Down
44(4)
Back and Forth
48(12)
Exercises and Remarks
60(11)
Algebraic Examples
71(44)
Quantifier Elimination
71(13)
Algebraically Closed Fields
84(9)
Real Closed Fields
93(11)
Exercises and Remarks
104(11)
Realizing and Omitting Types
115(60)
Types
115(10)
Omitting Types and Prime Models
125(13)
Saturated and Homogeneous Models
138(17)
The Number of Countable Models
155(8)
Exercises and Remarks
163(12)
Indiscernibles
175(32)
Partition Theorems
175(3)
Order Indiscernibles
178(11)
A Many-Models Theorem
189(6)
An Independence Result in Arithmetic
195(7)
Exercises and Remarks
202(5)
ω-Stable Theories
207(44)
Uncountably Categorical Theories
207(8)
Morley Rank
215(12)
Forking and Independence
227(9)
Uniqueness of Prime Model Extensions
236(4)
Morley Sequences
240(3)
Exercises and Remarks
243(8)
ω-Stable Groups
251(38)
The Descending Chain Condition
251(4)
Generic Types
255(6)
The Indecomposability Theorem
261(6)
Definable Groups in Algebraically Closed Fields
267(12)
Finding a Group
279(6)
Exercises and Remarks
285(4)
Geometry of Strongly Minimal Sets
289(26)
Pregeometries
289(4)
Canonical Bases and Families of Plane Curves
293(7)
Geometry and Algebra
300(9)
Exercises and Remarks
309(6)
A Set Theory 315(8)
B Real Algebra 323(6)
References 329(8)
Index 337