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Books > Science & Mathematics > Mathematics > Philosophy of mathematics
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Simplicity Theory (Hardcover)
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Simplicity Theory (Hardcover)
Series: Oxford Logic Guides, 53
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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 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.
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