Introduction to Model Theory - Philipp Rothmaler

Introduction to Model Theory

Buch | Hardcover
324 Seiten
2000
Taylor & Francis Ltd (Verlag)
978-90-5699-287-3 (ISBN)
143,40 inkl. MwSt
An introductory text, "Model Theory" investigates mathematical structures by means of formal languages. It avoids syntactical issues which are not too relevant to model theory. Selected exercises have hints and solutions and some reflect very recent research in the field.
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.

Rothmaler, Philipp

Basics, Structures, Languages, Semantics. Beginnings of Model Theory, The Finiteness Theorem, First Consequences of Finiteness Theorem, Malcev's Applications to Group Theory, Some Theory of Ordering. Basic Properties of Theories, Elementary Maps, Elimination, Chains. Theories and Types, Types, Thick and Thin Models, Countable Complete Theories. Two Applications, Strong Minimal Theories, Hints to Selected Exercise, Solutions for Selected Exercises.

Erscheint lt. Verlag 31.10.2000
Reihe/Serie Algebra, Logic and Applications
Verlagsort London
Sprache englisch
Maße 152 x 229 mm
Gewicht 653 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Logik / Mengenlehre
ISBN-10 90-5699-287-2 / 9056992872
ISBN-13 978-90-5699-287-3 / 9789056992873
Zustand Neuware
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