Announcements


The course begins on Tuesday 17th January, 10 am. See you there!

Forum

General


Description

This will be a 10 hour "version" of what was previously given (Spring 2008, Spring 2010) as a 20 hour course. However, I plan to be somewhat more ambitious, at the expense of leaving many details of the introductory material to be done in exercises. Among the new aspects of the new version will be the inclusion of stability theory. The first 5 hours will introduce model theory and stability theory, including stable groups. The last 5 hours will concern connections and applications, largely where groups of one form or the other are involved, and will be taken from among: geometric group theory, diophantine geometry over number fields and function fields (Manin-Mumford, Mordell-Lang), approximate subgroups,..
Semester

Spring 2012 (Monday, January 16 to Friday, March 23)

Timetable
  • Tue 10:05 - 10:55
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Students


Photo of Hawazin Alzahrani
Hawazin Alzahrani
(Manchester)
Photo of Robert Barham
Robert Barham
(Leeds)
Photo of Ahmet Cevik
Ahmet Cevik
(Leeds)
Photo of Cong Chen
Cong Chen
(Leeds)
Photo of Michal Ferov
Michal Ferov
(Southampton)
Photo of Andrew Furnas
Andrew Furnas
(Leeds)
Photo of Robert Henderson
Robert Henderson
(East Anglia)
Photo of Nicholas Loughlin
Nicholas Loughlin
(Newcastle)
Photo of Nathanael Mariaule
Nathanael Mariaule
(Manchester)
Photo of Gregory McKay
Gregory McKay
(East Anglia)
Photo of Ronnie Nagloo
Ronnie Nagloo
(Leeds)
Photo of Pedro Valencia
Pedro Valencia
(Leeds)
Photo of Dan Dan Yang
Dan Dan Yang
(York)
Photo of Rida-e Zenab
Rida-e Zenab
(York)


Prerequisites


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

Syllabus


beginitemize item textbfLectures 1 to 5: BASICS OF MODEL THEORY AND STABILITY THEORY: First order languages, structures and theories, compactness, types, saturation and homogeneity, stability, stable groups.
item textbfLecture 7 to 10: APPLICATIONS: I will cover 4 or 5 topics, explaining why and how material from the earlier lectures can give insights in areas of algebra, geometry, and number theory. More details will be given closer to the start date.
enditemize

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:

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.)

Assessment


The assessment will based on doing four assignments. Passing three out of these four assignments is required for a pass overall.
The assignments will be connected with filling in details and solving some problems related to basic material in the first past of the course, and can serve as a means for non-experts to gain some entry into and competence in general model theory.

Assignments


Assignment 1

Files:Exam paper
Deadline: Friday 23 March 2012 (944.3 days ago)


Assignment 2

Files:Exam paper
Deadline: Friday 23 March 2012 (944.3 days ago)


Assignment 3

Files:Exam paper
Deadline: Friday 23 March 2012 (944.3 days ago)


Assignment 4

Files:Exam paper
Deadline: Friday 23 March 2012 (944.3 days ago)


Files


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

Week(s)File
assignment1-2012.pdf
assignment2-2012.pdf
assignment3-2012.pdf
assignment4-2012.pdf
magic2012-handout.pdf
magic2012-lecturenotes.pdfL