Description: A first course in model theory focusing both on the foundations of the subject, and on several modern applications. Topics to be covered include:

• Review of basic notions and the Compactness Theorem

• Quantifier elimination and applications to algebra

• Types

• Saturated and homogeneous models

• Omitting types and prime models

• Indiscernibles and Morley’s Theorem (if time permits)
  

Prerequisites: It will be helpful for students enrolled to have experience in abstract algebra (e.g. previous or concurrent enrollment in MTH 516 is suggested).

Course text: We will mostly follow Model Theory: An Introduction by David Marker, Springer-Verlag, 2000.

Other popular introductory texts:

1. C.C. Chang and H.J. Keisler, Model Theory, Dover Publications; Third edition, 2012

2. W. Hodges, A Shorter Model Theory, Cambridge University Press, 1997.

3. B. Poizat, A Course in Model Theory: An Introduction to Contemporary Mathematical Logic, Springer-Verlag, 2000.

4. P. Rothmaller, Introduction to Model Theory, Gordon and Breach Science Publishers, 2000.
   

Grading/Homework: There will be a problem set due every two weeks or so. You are encouraged to work together on homework problems, but you should acknowledge that you have collaborated when you turn in the work.

Accommodations: UIC is committed to full inclusion and participation of people with disabilities in all aspects of university life. Students who face or anticipate disability-related barriers while at UIC should connect with the Disability Resource Center (DRC) at drc.uic.edu, drc@uic.edu, or at (312) 413-2183 to create a plan for reasonable accommodations. In order to receive accommodations, students must disclose disability to the DRC, complete an interactive registration process with the DRC, and provide their course instructor with a Letter of Accommodation (LOA). Course instructors in receipt of an LOA will work with the student and the DRC to implement approved accommodations.

• Handout 1

• Homework 1

• Homework 2

• Homework 3

• Homework 4

• Homework 5