• Propositional logic. In this section, we shall study propositional languages. We shall concentrate on trying to understand the meaning of the Compactness Theorem for propositional logic. Numerous applications of the Compactness Theorem will be presented, including an infinite analogue of the Four Color Theorem.

• First order logic. In this section, we shall try to understand the relationship between the syntax and semantics of first order languages. This study will culminate in Godel's Completeness and Compactness Theorems for first order logic.

• Applications of the Compactness Theorem. In this section, we shall present various applications of the Compactness Theorem for first order logic, including the existence of nonstandard models of arithmetic.

The term grade will be based on the results of the examinations and the solutions of the homework problems. We will have 2 midterm (80 minute) exams and a final exam. Homework be assigned during most lectures and will be collected each Wednesday. Here are the weights of the different components:

Lecture Notes:

• Basic Set Theory

• Functions

• Cantor-Bernstein

• Relations

• Propositional Logic

• Applications

• Konig's Lemma

• First Order Logic

• Compactness

• Logical Axioms

• Completeness Theorem