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Math 6000: Model Theory, Spring 2014


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: 
A Course in Model Theory, by K. Tent and M. Ziegler (2012).
The CU library offers electronic access to this book.

Supporting materials: 
Don Monk has a nice set of notes, which covers some basic material omitted from our text.

The Wikipedia page for model theory has good list of 18 references to textbooks/sets of notes, including 6 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 every other week starting the second week. Solutions to old assignments will be posted when they are in final form. You should read your classmates' solutions.