MAGIC004: Applications of model theory to algebra and geometry

Course details

A specialist MAGIC course


Spring 2022
Monday, January 31st to Friday, March 25th; Monday, April 25th to Friday, May 6th


Live lecture hours
Recorded lecture hours
Total advised study hours


14:05 - 14:55 (UK)


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. 


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


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). 


  • Dr Vincenzo Mantova

    Dr Vincenzo Mantova

    University of Leeds


No bibliography has been specified for this course.


The assessment for this course will be released on Monday 9th May 2022 at 00:00 and is due in before Monday 23rd May 2022 at 11:00.

Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).

You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).

If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.

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


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