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Model Theory : An Introduction de David Marker

Model Theory : An Introduction: Graduate Texts in Mathematics, cartea 217

Autor David Marker
en Limba Engleză Paperback – dec 2010
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
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Paperback (1) 44028 lei  6-8 săpt.
  Springer – dec 2010 44028 lei  6-8 săpt.
Hardback (1) 44545 lei  6-8 săpt.
  Springer – 21 aug 2002 44545 lei  6-8 săpt.

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Specificații

ISBN-13: 9781441931573
ISBN-10: 1441931570
Pagini: 356
Ilustrații: VIII, 345 p.
Dimensiuni: 155 x 235 x 19 mm
Greutate: 0.5 kg
Ediția:Softcover reprint of hardcover 1st ed. 2002
Editura: Springer
Colecția Springer
Seria Graduate Texts in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Graduate

Cuprins

Structures and Theories.- Basic Techniques.- Algebraic Examples.- Realizing and Omitting Types.- Indiscernibles.- ?-Stable Theories.- ?-Stable Groups.- Geometry of Strongly Minimal Sets.

Recenzii

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)

Textul de pe ultima copertă

This book is a modern introduction to model theory which 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.

David Marker is Professor of Mathematics at the University of Illinois at Chicago. His main area of research involves mathematical logic and model theory, and their applications to algebra and geometry. This book was developed from a series of lectures given by the author at the Mathematical Sciences Research Institute in 1998.

Caracteristici

Includes supplementary material: sn.pub/extras

Descriere

Descriere de la o altă ediție sau format:

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