## Professor Andre Scedrov

Office: Room 4E6 in David Rittenhouse Laboratory
Telephone: eight five nine eight three ( Math. Dept. Office: eight eight one seven eight )
Fax: three four zero six three
E-mail: lastname at math
Office Hours: By appointment

From Encyclopaedia Britannica: Gödel's proof, which states that within any rigidly logical mathematical system there are propositions (or questions) that cannot be proved or disproved on the basis of the axioms within that system; that is, such a system cannot be proved simultaneously to be complete and consistent. This proof has become a hallmark of 20th-century mathematics, and its repercussions continue to be felt and debated.

## Topics

Chapters 0 - 3 from Enderton:

• Propositional Logic: Propositions and Connectives, Semantics, Natural Deduction, Completeness.
• Predicate Logic: Quantifiers, Structures, Semantics, Natural Deduction, The Completeness Theorem, Compactness and Skolem-Löwenheim Theorems, Skolem Functions.
• Undecidability and Incompleteness: Turing Machines, Undecidability of Predicate Logic, Gödel's First and Second Incompleteness Theorems.

## Homework Due in Class on Wednesday, September 24

The following problems from Enderton, 2-nd edition:

• p. 27: Exercises 1, 2ab, 3ab, 5ab
• p. 29: Exercise 15.
• p. 65: Exercise 2.
This is the complete list of assignments due September 24, 2008.

## Homework Due in Class on Monday, October 6

The following problems from Enderton, 2-nd edition:

• p. 52: Exercise 2.
• p. 53: Exercise 9b.
• p. 66: Exercises 8, 11ab.
In addition, also prove the following:
• There are no integers k and n, with n not equal to 0, such that 2 * (n^2) = k^2. That is, square root of 2 is not a fraction.
This is the complete list of assignments due October 6, 2008.

## Take-Home Midterm Due in Class on Wednesday, October 29

The following problems from Enderton, 2-nd edition:

• p. 66: Exercise 12abc.
• pp. 101-104: Exercises 16, 25ab, 27, 28abc.
• p. 146: Exercises 7bc, 8, 9abc.
This is the complete list of take-home midterm assignments due in class on Wednesday, October 29, 2008.

## Take-Home Final Exam Due in DRL 4E6 at 11 am on Monday, December 15

The following problems from Enderton, 2-nd edition:

• pp. 223-224: Exercises 2, 4, 5.
• p. 234: Exercises 1, 2.
• Optional problems for extra credit: p. 245: Exercises 1, 2, 3.
This is the complete list of take-home final exam assignments due in DRL 4E6 at 11 am on Monday, December 15.