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  3. Model Theory, Algebra, and Geometry
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  • Publisher:
    Cambridge University Press
    Publication date:
    June 2025
    July 2000
    ISBN:
    9781009701464
    9780521780681
    9780521143493
    DOI:
    https://doi.org/10.1017/9781009701464
    Dimensions:
    (247 x 174 mm)
    Weight & Pages:
    0.46kg, 236 Pages
    Dimensions:
    (234 x 156 mm)
    Weight & Pages:
    0.34kg, 236 Pages
    • Subjects:
    Mathematics, Logic, Categories and Sets, Real and Complex Analysis
    Series:
    Mathematical Sciences Research Institute Publications
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    Subjects:
    Mathematics, Logic, Categories and Sets, Real and Complex Analysis
    Series:
    Mathematical Sciences Research Institute Publications
    Information

    Book description

    Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields, to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases (such as the latter) it is the most abstract aspects of model theory which are relevant. This book, originally published in 2000, arising from a series of introductory lectures for graduate students, provides the necessary background to understanding both the model theory and the mathematics behind these applications. The book is unique in that the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations) is covered and diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) are introduced and discussed, all by leading experts in their fields.

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