Kurt Gödel.

**
Mathematical Logic, MA 430, CRN 20084 and 20442, Fall 2009
**

- R. Cori and D. Lascar: Mathematical logic, A course with exercises; Vol. I
- H. Enderton: A mathematical introduction to logic.
- H.-D. Ebbinghaus, J. Flum, W. Thomas: Mathematical logic.

**Lecture notes:**- Propositional logic
- Zorn's Lemma
- Compactness Theorem
- Proofs in propositional logic
- The tableau method
- Predicate logic
- Formulas of a first order language
- First order theories
- First order structures
- Model theory
- Formal proofs
- Herbrand's Theorem
- The tableau method for first order logic
- The compactness theorem for first order logic

**Prepare the following set of exercises for Wednesday. I will go through some of them on the blackboard:**

**Exam syllabus:**Chapters 1,2,3,4,5 in Srivastava's book, plus all material covered in class and in homework exercises.

Students taking the class for 4 credit hours will have to do additional work, which will be decided soon.

**Course hours:**Monday - Wednesday - Friday, 9:00-9:50 AM. Addams Hall 306

**Office hours:**In my office SEO 416.- Tuesday 2:00-3:30.

**Problem sessions:**- Monday, Sept. 21st, SEO 612, 4-5 PM..
- No problem session Monday Sept. 28th.

**Reading:**I will assign material from the book to be read every week before being presented in class. We shall not follow the organisation of the material in Srivastava's book too closely and the lectures and homework exercises will expand on the book. Therefore, it is strongly encouraged that you attend every class and take notes. A good strategy is to read every section before it is covered it class, take notes and gain additional understanding during class, and the reread the section and do the assigned homework exercises at the end of the week. The material covered in exercises constitute an integral part of the exam syllabus and will greatly help you assimilate the theoretical material.

**Homework:**There will be a number homework sets due in the course of the semester. These should be handed in to me at the beginning of class on the due date, which will generally be on Wednesdays. No late homework will be accepted and any homework handed in after the deadline will be credited for 0 points. When calculating the homework grade, the lowest score on a homework set will be dropped. So, e.g., if you have missed one homework set, then this will be counted as your lowest score.

**Midterms:**There will be two midterms each taking place during regular class hours. These will take place on:

- 1st midterm: Monday, October 12th. Syllabus: Everything covered about propositional logic.
- 2nd midterm: Friday, November 6th.

To be excused from a midterm you will need to provide a valid excuse and a letter from the doctor to this effect. You will not have the chance to make up an exam, so if you are excused from a midterm, your midterm grade will be the score on your other midterm. It is your responsibility to be in time for an exam, not your alarm clock's.

**Final exam:**Will take place Tuesday, December 8th, 10:30 - 12:30.

**Grade:**Your grade will be a weighted average of your homework, midterm, and final grades calculated as follows:

- Homeworks: 20 %
- Midterms: 40 %
- Final: 40 %

**Weekly programme:**

- Week beginning on August 24th:
*Syntax and semantics of propositional logic. Sections 1.1, 1.2, 1.3, 3.1, 3.2.* - Week beginning on August 31st:
*Syntax and semantics of propositional logic. Sections 1.1, 1.2, 1.3, 3.1, 3.2.* - Week beginning on September 7th:
*Compactness and proofs for propositional logic. Sections 3.3, 3.4, 3.5.* - Week beginning on September 14th:
*The completeness theorem for propositional logic. Sections 3.4, 3.5, 3.6.* - Week beginning on September 21st:
*We finish with the completeness theorem for propositional logic. Section 3.6.* - Week beginning on September 28th:
*The tableau method and syntax of first order logic.* - Week beginning on October 5th:
*Preparation for midterm.* - Week beginning on October 12th:
*Midterm and continuation of syntax and semantics for first order logic, Chapter 1 and 2.* - Week beginning on October 19th:
*Chapter 2.* - Week beginning on October 26th:
*Chapter 4.* - Week beginning on November 2nd:
*Chapter 4 and second midterm.* - Week beginning on November 9th:
*Chapter 4.* - Week beginning on November 16th:
*Chapter 5.* - Week beginning on November 23rd:
*Chapter 5.* - Week beginning on November 30th:
*Chapter 5.*

**Homework exercises:**

- Due Wednesday September 2nd: pdf
- No homework is due on Wednesday September 9th because of labour day.
- Due Wednesday September 16th: pdf
- Due Wednesday September 23rd: Do the exercise sheet handed out in class plus the following exercises, pdf
- Due Wednesday September 30th: pdf
- Due Wednesday October 7th: Part 1, Part 2
- No homework due on Wednesday October 14th due to the mid-term.
- Due Wednesday October 21st: pdf
- No homework will be due on October 28th.
- Due Wednesday November 4th: pdf. Solutions.
- No homework will be due on November 18th.
- Due Wednesday November 25th: Part 1, Part 2. Please note the use of a slightly non-standard symbol for equality.