## 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 and that, therefore, it is uncertain that the basic axioms of arithmetic will not give rise to contradictions. 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.

## Take-Home Midterm Due in Class on Friday, March 8

The following problems from Enderton, 2nd edition:

• p. 66: Exercises 10 ab, 11 ab, 12 abc.
• pp. 100-104: Exercises 16, 20 ab, 25 ab, 27, 28 abc.
• p. 146: Exercises 7 bc, 8, 9 abc.
This is a complete list of assignments due March 8, 2002.

## Take-Home Final Due in DRL 4E6 on Tuesday, April 30 at 12 noon

The following problems from Enderton, 2nd edition:

• p. 163: Exercises 4, 9, 10.
• pp. 223-224: Exercises 2, 4, 5, 6, 8, 9.
• p. 234: Exercises 1, 2.
• Optional problems for extra credit: p. 245: Exercises 1, 2, 3.
This is a complete list of assignments due April 30, 2002.