Philipp Rothmaler

Introduction to Model Theory (eBook, ePUB)

• Format: ePub

Produktbeschreibung

Model theory is used to investigate mathematical structures by means of formal languages, and first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic. Avoiding syntactical issues, author proves the compactness theorem via the ultraproduct technique, which leads fairly quickly to algebraic applications like Malcev's local theorems and eventually to Hilbert's Nullstellensatz. The author obtains Steinitz dimension theory for field extensions as a special case of a more general model-theoretic treatment of strongly minimal theories. The final chapter explores the models of the first-order theory of the integers as an abelian group.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 324
• Erscheinungstermin: 7. Dezember 2018
• Englisch
• ISBN-13: 9781351990318
• Artikelnr.: 73153958

Autorenporträt

Rothmaler, Philipp

Inhaltsangabe

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.