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.
SemesterSpring 2016 (Monday, January 11 to Friday, March 18) 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).
Students
Bibliography
Note: Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.) AssessmentThe assessment for this course will be via a single take-home paper in April with 2 weeks to complete and submit online.
There will be 5 questions of which you should answer no more than 4. You will need the equivalent of 2 questions to pass.
Exam Applications of Model Theory to Algebra and Geometry
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