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Simplicity Theory Byunghan Kim

Simplicity Theory

Byunghan Kim

Published June 12th 2014
ISBN : 9781299963702
ebook
235 pages
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 About the Book 

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 mathematicalMoreModel 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 class includes 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 the uniform 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 graduate students working on model theory.