## Preliminary Syllabus for Math 461: Mathematical Logic

## Spring 2021

**Textbook**: Enderton, * A mathematical introduction to logic*, Academic Press.

**Meeting times**: The lectures will be held as Zoom meetings every Monday and Wednesday from 1:40pm until 3:00pm

**Main course topics**:

**Elementary set theory.** After a review of the
basic properties of functions, relations and structures, we will consider the notions of a countable and an uncountable set.

**Propositional logic.** In this section, we will study
propositional languages. We will 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 will 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 will present various applications of the Compactness Theorem
for first order logic, including the existence of nonstandard models
of arithmetic.

The final grade will be based on the results of the examinations and the solutions of the weekly homework problems. We will have two midterm exams and a final exam. Here are the weights of the different components of the course:

- Homework 20%
- First Midterm 20%
- Second Midterm 20%
- Final Exam 40%