Thoralf Skolem Alonzo Church

Mathematical Logic (Metamathematics I), MATH 502, Fall 2011

Instructor: Christian Rosendal, room 416 SEO

Lectures: MWF 11:00-11:50 in TH 117.

Office hours: Monday and Wednesday 1:30 PM - 2:30 PM or by appointment. Please let me know after class if you plan to come.

Course description:
This is the standard graduate course on mathematical logic beginning with a brief introduction to propositional logic and ending with a thorough treatment of Gödel's incompleteness Theorem and decidability problems in logic.

Topics
• Propositional logic
• Predicate logic and proofs
• First order structures
• Completeness and compactness of predicate logic
• Elementary model theory and the Löwenheim-Skolem Theorem
• Computability, Decidability and Gödel's incompleteness Theorem
Literature:
There is no textbook for the course. Instead we shall follow a set of notes by Lou van den Dries, which are available here.

Homework: The grade for the course is based on written homework sets that will be assigned in the course of the semester. I will list these here in due course. Please hand these in during class on the due date or leave them in my mailbox in SEO.
• 1st homework set due on Friday Sept. 9th: Page 19, exercises 1,3,5; page 24, exercise 2; page 30, exercises 2,3.
• 2nd homework set due on Friday Sept. 23rd: Page 34, exercises 5,6; page 41, exercises 1,9
• 3rd homework set due on Friday Oct. 7th: Page 49, exercises 1,2; page 53, exercises 1,4.
• 4th homework set due on Friday Oct. 21st: Page 64, exercises 1,2; page 65, exercises 1,2.
• 5th homework set due on Friday Nov. 4th: Page 69, exercises 1,3,5; page 74, exercise 1, page 89, exercises 1,4.
• 6th homework set due on Friday Nov. 18th: Page 89, exercises 5,6; page 99, exercise 1; page 105, exercises 1,2.
• 7th homework set due on Wednesday Nov. 30th: Page 110, exercises 1,2.
Other exercises: Apart from the exercises that are to be handed in as homework, you are very strongly advised to at least attempt or think about all the remaining exercises in the notes. The results of the may be used later on and will increase your understanding of the material. Note that many of these are just formulated as statements where you are supposed to fill in details of the construction or proof.

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