Course
Home
Syllabus
Lecture Topics
Homework
Policies
Links
Problem of the Month
Math Club (QED)
Putnam Competition (Dr. Wise)
Math Department Tutor List
|
|
Math 6000: Model Theory,
Spring 2020
|
|
Syllabus
|
|
|
Course description:
Proves the compactness theorem,
showing the essential finiteness of logical implication.
Proves many basic properties of theories, showing how
the syntactic form of statements influences their
behavior with respect to different models. Finally,
studies properties of elements that cannot be stated
by a single formula (the type of the element) and shows
it can be used to characterize certain models.
|
Prerequisites:
Graduate students only.
|
|
Text:
Model Theory: An Introduction (Graduate Texts in Mathematics, Vol. 217)
, by D. Marker (2002).
The CU library offers the PDF of the full text
here for no charge.
Let me know if you have trouble downloading it.
A physical copy of the book is on 2 hour reserve at Gemmill library.
|
Supporting materials:
Don Monk has a nice set of
notes.
The
Wikipedia page for
model theory
has good list of references to textbooks/sets of notes, including
some that are free online. Missing from the
Wikipedia page are the free books/notes:
Model Theory by Simpson
Fundamentals of Model Theory by Weiss and D'Mello
Elementary Model Theory by McNulty
Guram Bezhanishvili has a nice
historically-oriented discussion about
Henkin's proof of the Completeness Theorem
and the Löwenheim-Skolem Theorem. Follow
this
link and click on Project 13.
|
Homework:
If you are enrolled for credit I will ask you to solve
some problems. You will be asked to work on the problems
in small groups of 2-3. Different groups will be assigned different problems,
and groups will change with each assignment.
You will typically have a week for your group to solve its assigned
problem(s) and submit the solution(s).
(This deadline is not strict. but
I'll check in with you if I don't get
solutions within a couple days of the due date.)
If you are solving Problem M of HW assigment N, please submit
the solution as a PDF file called "modthNpM.pdf"
(which abbreviates "model theory
assignment N, problem M"). At the top of the first page of the solution
please include the names of all group members and the
assigment number.
After receiving your solution I will correspond
with you about improvements and corrections,
if I can think of any. This step
in the process should take at most one week.
You are not obligated to take any of my advice,
but if one of my comments involves a correction,
then you should correct that part in some way.
For example, if I say "Here is a shorter way to do it",
you don't have to change anything unless you want to.
If I say "The first displayed equation is wrong. Here is
how to fix it …", then you should fix the
error, not necessarily along the lines of my suggestion.
If you believe that one of my criticisms is
incorrect, then you do not have to change your work,
but you do have to explain why the criticism is incorrect.
New assignments will be posted regularly
starting the second week. Solutions to old assignments will
be posted when they are in final form.
You should read your classmates' solutions.
|
|
|