MAGIC004: Applications of model theory to algebra and geometry

Course details

Semester

Autumn 2017
Monday, October 9th to Friday, December 15th

Hours

Live lecture hours
10
Recorded lecture hours
0
Total advised study hours
0

Timetable

Fridays
12:05 - 12:55

Description

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.

Prerequisites

Some familiarity with first order logic would be helpful but not essential.

Syllabus

Lectures 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).

Lecturer

  • Dr Vincenzo Mantova

    Dr Vincenzo Mantova

    University
    University of Leeds

Bibliography

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Assessment

The assessment for this course will be released on Monday 8th January 2018 and is due in by Sunday 21st January 2018 at 23:59.

The assessment for this course will be via a single take-home paper in January 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.

Please note that you are not registered for assessment on this course.

Files

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Lectures

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