Home Page for Math 711: Model Thoery Winter 2011-2012


Textbook: Model theory: an introduction, David Marker, Springer GTM 217.
Course objective: To learn the ideas an techniques of model theory and its applications to algebraic structures.

Instructor: Dr. D. Haskell, HH316, ext.27244

Course meeting time: W 9:30--10:30, F 9:30--11:30 in HH410
E-mail: haskell@math.mcmaster.ca
Office hours: M 10:30-11:30, W 10:30-12:30 or by appointment

Course requirements, in brief (consult the course information sheet  for more detailed information).
Attendance and class participation: 20%
Homework: 40%
Final: 40%

Announcements

The last class of the semester will be on Thursday, 5 April, 1:30-3:00. I am not sure if Wednesday is an official class day or not, but anyway, there will be no class on Wednesday, 4 April.

Homework assignments (Problems in the Marker textbook.)

Homework 1: 1.4.2, 1.4.8, 1.4.11, 1.4.12, 1.4.16, 2.5.2, 2.5.8 due Friday, 20 January 2012

Homework 2: 2.5.9, 2.5.11, 2.5.14, 2.5.15, 2.5.17, 2.5.28 due Friday, 3 February 2012 (except I will be away, so the following Monday)

Homework 3: 3.4.3, 3.4.4, 3.4.6, 3.4.12, 3.4.15 (lots of typos in this last problem) due Friday, 2 March (revised to Tuesday 6 March

Homework 4: 3.4.24, 4.5.1, 4.5.4, 4.5.13  due Monday 26 March.

Homework 5: 4.5.24, 4.5.25 due Monday April 9

Course Calendar

The course calendar is subject to change as we move through the semester. Changes in homework due dates will be announced in the announcements section of this webpage.

Dates
  Wednesday Friday
 Reading
Week 1
Jan 3 - 6
 review of first-order logic
 definability and interpretability
 Chapter 1
Week 2
Jan 9 - 13
 theories: divisible torsion-free abelian groups and algebraically closed fields
 compactness, completeness, categoricity, Vaught's test, Ax's thoerem
 2.1 and 2.2
Week 3
Jan 16 - 20
Lowenheim-Skolem theorems
 2.3
Week 4
Jan 23 - 27
 discussion of homework 2
 back and forth technique, and Ehrenfeucht-Fraisse games
 2.4
Week 5
Jan 30 - Feb 3
techniques for proving quantifier elimination, examples
 3.1
Week 6
Feb 6 - 10
 real closed fields
 algebraically closed and real closed fields
 3.2 and 3.3
Week 7
Feb 13 - 17
 QE in theories with equivalence relations
 more about ACF and RCOF
3.2 and 3.3
Feb 20 - 24
 READING WEEK
 READING WEEK
Week 8
Feb 27 - Mar 2
 discussion of homework 3
 types
 4.1
Week 9
Mar 5 - 9
 examples of types
 omitting types
 4.2
Week 10
Mar 12 - 16
homogeneous models
 4.2
Week 11
Mar 19 - 23
saturated models
 4.3
Week 12
Mar 26 - 30
differentially closed fields
Week 13
Apr 2 - 6