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General


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.

Semester

Spring 2016 (Monday, January 11 to Friday, March 18)

Timetable

  • Thu 11:05 - 11:55

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


Immanuel Halupczok
Email I.Halupczok@leeds.ac.uk
Phone 0113 34 37567


Students


Photo of Abeer Al Balahi
Abeer Al Balahi
(East Anglia)
Photo of Mehsin Al-Showali
Mehsin Al-Showali
(Leicester)
Photo of Asma Almazaydeh
Asma Almazaydeh
(Leeds)
Photo of Carolyn Barker
Carolyn Barker
(Leeds)
Photo of Daniel Cheng
Daniel Cheng
(York)
Photo of Tanmay Inamdar
Tanmay Inamdar
(East Anglia)
Photo of Ewan Johnstone
Ewan Johnstone
(Liverpool)
Photo of Konrad Krolicki
Konrad Krolicki
(Lancaster)
Photo of Brendan Nolan
Brendan Nolan
(*External)
Photo of Francesco Parente
Francesco Parente
(East Anglia)
Photo of Angelo Rendina
Angelo Rendina
(Sheffield)
Photo of ANON STUDENT
ANON STUDENT
(*External)
Photo of Dionysios Syrigos
Dionysios Syrigos
(Southampton)
Photo of Matthew Waller
Matthew Waller
(Nottingham)
Photo of Ariel Weiss
Ariel Weiss
(Sheffield)


Bibliography


Model theory: an introductionMarker
A course in model theory: an introduction to contemporary mathematical logicPoizat and Klein
Lecture notes in Model TheoryA. Pillay


Note:

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Assessment



The 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

Files:Exam paper
Released: Monday 18 April 2016 (489.2 days ago)
Deadline: Friday 29 April 2016 (477.2 days ago)
Instructions:

Please answer no more than 4 out of the 5 questions. All questions carry equal marks.



Files


Files marked L are intended to be displayed on the main screen during lectures.

Week(s)File
slides-printable.pdf
0slides-uncover-stepwise.pdfL
0slides.pdfL
1exercises1.pdf
2-3exercises2.pdf
4exercises3.pdf
6exercises4.pdf


Recorded Lectures


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