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Model Theory: An Introduction by David Marker, graduate texts in mathematics HC.
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Item specifics
- Condition
- Book Title
- Model Theory : An Introduction
- ISBN-13
- 9780387987606
- Subject
- Mathematics
- ISBN
- 9780387987606
- Series
- Graduate Texts in Mathematics Ser.
- Publication Year
- 2002
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Publication Name
- Model Theory : an Introduction
- Item Length
- 9.3in
- Publisher
- Springer New York
- Item Width
- 6.1in
- Item Weight
- 24.7 Oz
- Number of Pages
- VIII, 345 Pages
About this product
Product Information
Model theory is a branch of mathematical logic where we study mathem- ical structures by considering the ?rst-order sentences true in those str- turesandthesetsde'nableby'rst-orderformulas.Traditionallytherehave been two principal themes in the subject: *startingwithaconcretemathematicalstructure,suchasthe'eldofreal numbers, and using model-theoretic techniques to obtain new information about the structure and the sets de'nable in the structure; * looking at theories that have some interesting property and proving general structure theorems about their models. A good example of the ?rst theme is Tarski's work on the ?eld of real numbers. Tarski showed that the theory of the real ?eld is decidable. This is a sharp contrast to G¨ odel's Incompleteness Theorem, which showed that the theory of the seemingly simpler ring of integers is undecidable. For his proof, Tarski developed the method of quanti'er elimination which can be n used to show that all subsets of R de'nable in the real ?eld are geom- rically well-behaved. More recently, Wilkie [103] extended these ideas to prove that sets de'nable in the real exponential ?eld are also well-behaved. ThesecondthemeisillustratedbyMorley'sCategoricityTheorem,which says that if T is a theory in a countable language and there is an uncou- able cardinal ? such that, up to isomorphism, T has a unique model of cardinality ?,then T has a unique model of cardinality ? for every - countable'.ThislinehasbeenextendedbyShelah[92],whohasdeveloped deep general classi'cation results.
Product Identifiers
Publisher
Springer New York
ISBN-10
0387987606
ISBN-13
9780387987606
eBay Product ID (ePID)
2274201
Product Key Features
Publication Name
Model Theory : an Introduction
Format
Hardcover
Language
English
Series
Graduate Texts in Mathematics Ser.
Publication Year
2002
Type
Textbook
Number of Pages
VIII, 345 Pages
Dimensions
Item Length
9.3in
Item Width
6.1in
Item Weight
24.7 Oz
Additional Product Features
Series Volume Number
217
Number of Volumes
1 Vol.
Lc Classification Number
Qa8.9-10.3
Reviews
From the reviews:MATHEMATICAL REVIEWS"This is an extremely fine graduate level textbook on model theory. There is a careful selection of topics…There 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 Hrushovski's 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 author's 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), From the reviews: MATHEMATICAL REVIEWS "This is an extremely fine graduate level textbook on model theory. There is a careful selection of topics...There 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 Hrushovski's 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 author's 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), From the reviews: MATHEMATICAL REVIEWS "This is an extremely fine graduate level textbook on model theory. There is a careful selection of topics…There 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 Hrushovski's 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 author's 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)
Table of Content
Structures and Theories.- Basic Techniques.- Algebraic Examples.- Realizing and Omitting Types.- Indiscernibles.- ?-Stable Theories.- ?-Stable Groups.- Geometry of Strongly Minimal Sets.
Copyright Date
2002
Topic
Logic
Lccn
2002-024184
Dewey Decimal
511.3
Intended Audience
Scholarly & Professional
Dewey Edition
23
Illustrated
Yes
Genre
Mathematics
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