eBook - PDF

Introduction to Model Theory

Name: Introduction to Model Theory
ISBN: 9780429668500

Philipp Rothmaler,

324 pages
English
PDF
Available on iOS & Android

eBook - PDF

Introduction to Model Theory

Philipp Rothmaler,

About this book

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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Yes, you can access Introduction to Model Theory by Philipp Rothmaler in PDF and/or ePUB format, as well as other popular books in Mathematics & Applied Mathematics. We have over one million books available in our catalogue for you to explore.