Description: A first course in mathematical logic. We will introduce the fundamental themes of mathematical logic, discuss their interconnections with several other areas of mathematics and examine the power and limits of formal methods. Topics to be covered include:

• Mathematical structures

• Formal proofs

• Godel's Completeness Theorem

• The Compactness Theorem and elementary model theory

• Model theory of algebraically closed fields

• models of computation, Church's Thesis

• Universal machines and undecidability

• Recursively enumerable and arithmetic sets

• Godel's Incompleteness Theorem

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 closely follow David Marker's 502 lecture notes (here).

Other popular introductory texts:

1. N. Cutland, Computability: An introduction to recursive function theory, Cambridge University Press, 1986.

2. H.-D. Ebbinghaus, J. Flum and W. Thomas, Mathematical Logic Second Edition, Springer-Verlag, 1994

3. R. Kaye, Models of Peano Arithmetic, Oxford University Press, 1991.

4. D. Marker, Model Theory: An Introduction, Springer, 2012.
   

Grading/Homework: The grade for the course is based on about 8 written homework sets that will be assigned in the course of the semester. 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.

• Homework 1 - Due Wednesday September 7 in class.

• Homework 2 - Due Monday September 19 in class.

• Homework 3 - Due Monday October 3 in class.

• Homework 4 - Due Wednesday October 19 in class.

• Homework 5

• Homework 6

• Homework 7

• Homework 8