Applications of model theory to algebra and geometry (MAGIC004) |
GeneralDescription
This course is aimed at PhD students, not necessarily working in model
theory, but working in areas potentially linked to model theory (e.g.
other parts of logic, or parts of algebra, algebraic geometry, number
theory, combinatorics). The first 5 lectures will introduce
fundamental model-theoretic concepts. The second part of the course
will explore various `tameness’ conditions on first order theories
(e.g. concepts associated with model-theoretic stability theory and
its extensions), with a focus on examples from algebra, especially
fields (e.g. algebraically closed, real closed and p-adically closed
fields, and pseudofinite fields). A goal will be to exhibit
potentially applicable methods.
SemesterAutumn 2017 (Monday, October 9 to Friday, December 15) Timetable
PrerequisitesSome familiarity with first order logic would be helpful but not essential.
SyllabusLectures 1—5: BASICS OF MODEL THEORY AND STABILITY THEORY: First order
languages, structures and theories, compactness, types, saturation and
homogeneity, quantifier elimination.
Lectures 6—10: TAME THEORIES, EXAMPLES, APPLICATIONS: uncountable
categorical and strongly minimal theories; stable, o-minimal, simple,
and NIP theories; model-theoretic notions of independence and
dimension, and their interpretation in algebraically important
structures (e.g. algebraically closed and real closed fields).
Bibliography
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