Introduction to Model Theory

Philipp Rothmaler

ISBN 10: 9056993135 / ISBN 13: 9789056993139

Published by CRC Press, 2000

About this Item

Introduction to Model Theory | Philipp Rothmaler | Taschenbuch | Englisch | 2000 | CRC Press | EAN 9789056993139 | Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, 36244 Bad Hersfeld, gpsr[at]libri[dot]de | Anbieter: preigu Print on Demand.

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Bibliographic Details

• Title: Introduction to Model Theory
• Publisher: CRC Press
• Publication Date: 2000
• Language: English
• ISBN 10: 9056993135
• ISBN 13: 9789056993139
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 229W x 152H x 19D millimeters 229 millimeters width by 152 millimeters height by 19 millimeters depth
• Weight: 528 grams
• Seller catalogs:
  • Bücher

About this title

Synopsis

Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.

About the Author

Rothmaler, Philipp