Course

Home

Syllabus

Lecture Topics

Homework

Policies




Math 6000: Model Theory, Spring 2024


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 4 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 Projects: 
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. 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 assignment 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 assignment 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. Solutions to old assignments will be posted when they are in final form. To permit me to post your completed, graded projects so that all students can read them, please fill out this form and send it back to me. Let me explain how to fill out the form.

  • In Part I, fill out your student information on the lines on the left.
  • For the recipient information, just write

    Students of Math 6000, Spring 2024

    on the name line. The rest of the recipient information may be left blank.

  • For Education record information to be released check the box by Other specific information to be released. Then fill in the following blank with

    Completed, graded homework projects.

  • For Purpose of release write

    To share completed, graded projects with classmates.

  • This form should be signed and returned to me (preferably electronically). I do not need you to include a photo ID when you send it to me.

    Dates: 
    MLK Jr (no class): Jan 15 (Monday)
    First day of classes: Jan 16 (Tuesday)
    Last day to drop without penalty: Jan 31 (Wednesday)
    Spring Break (no class): Mar 25-29 (Monday-Friday)
    Last day of classes: May 2 (Thursday)

    WWW: 
    Information concerning our class will be posted on my teaching web page under the link for Teaching. A copy of any document I hand out in class will be accessible from this page.