Introduction to Model Theory /
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| Format: | eBook |
| Language: | English |
| Published: |
Boca Raton, FL :
CRC Press,
[2018].
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| Edition: | First edition. |
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| Online Access: | Connect to the full text of this electronic book |
| Abstract: | 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. |
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| Physical Description: | 1 online resource (324 pages) |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781351990318 1351990314 9781315273822 1315273829 9780429668500 0429668503 9781351993197 1351993194 |