Simplicity Theory

Hardcover | November 14, 2013

byByunghan Kim

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Model theory, a major branch of mathematical logic, plays a key role connecting logic and other areas of mathematics such as algebra, geometry, analysis, and combinatorics. Simplicity theory, a subject of model theory, studies a class of mathematical structures, called simple. The classincludes all stable structures (vector spaces, modules, algebraically closed fields, differentially closed fields, and so on), and also important unstable structures such as the random graph, smoothly approximated structures, pseudo-finite fields, ACFA and more. Simplicity theory supplies theuniform model theoretic points of views to such structures in addition to their own mathematical analyses. This book starts with an introduction to the fundamental notions of dividing and forking, and covers up to the hyperdefinable group configuration theorem for simple theories. It collects up-to-date knowledge on simplicity theory and it will be useful to logicians, mathematicians and graduatestudents working on model theory.

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Model theory, a major branch of mathematical logic, plays a key role connecting logic and other areas of mathematics such as algebra, geometry, analysis, and combinatorics. Simplicity theory, a subject of model theory, studies a class of mathematical structures, called simple. The classincludes all stable structures (vector spaces, mod...

Byunghan Kim is Professor of Mathematics at Yonsei University in Seoul, Korea

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Format:HardcoverDimensions:240 pages, 9.21 × 6.14 × 0.98 inPublished:November 14, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198567383

ISBN - 13:9780198567387

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Table of Contents

Introduction1. Dividing, Forking, and Simplicity2. Lascar Strong Types and Type-Amalgamation3. Hyperimaginaries and canonical bases4. Elimination of hyperimaginaries5. Constructing simple structures6. Groups7. A geometry of forking8. Generalized amalgamation and the group