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Model Theory, Algebra, and Geometry

  • Category: Mathematics
  • Pages: : 236 pages
  • File type: : PDF Files

Read and download free eBook intituled Model Theory, Algebra, and Geometry in format : PDF Files – : 236 pages created by .

Model theory is a branch of mathematical logic that has found applications in several areas of algebra and geometry. It provides a unifying framework for the understanding of old results and more recently has led to significant new results, such as a proof of the Mordell-Lang conjecture for function fields in positive characteristic. Perhaps surprisingly, it is sometimes the most abstract aspects of model theory that are relevant to those applications.

This book gives the necessary background for understanding both the model theory and the mathematics behind the applications. Aimed at graduate students and researchers, it contains introductory surveys by leading experts covering the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations), and introducing and discussing the diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) to which the model theory is applied.

The book begins with an introduction to model theory. It then broadens into three components: pure model theory, geometry, and the model theory of fields.

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Model Theory, Algebra, and Geometry

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