MTH 246: LOGIC AND SET THEORY

A Mathematical Introduction To Logic (second edition), by Herbert B. Enderton

We will cover Chapters 1 and 2 thoroughly and go through as much of Chapter 3 as time allows.

Topics covered: As the title suggests, this is a course in mathematical logic. After a brief review of the basics of set theory, we study the simple sentential (sentence-based) logic of objects and connective symbols ("A implies B", etc.). This, however, turns out to be insufficient for describing the properties of objects like the natural numbers, which require quantifiers ("for ever", "there exists"). This leads to the introduction of first order logic. First-order logic, as studied in this class, has the pleasant property of completeness, which means, roughly, that there exist formal proofs of true statements (this is called Godel's completeness theorem). However, in any sufficiently rich, consistent first-order system, there will be statements that are neither true nor false (this is called Godel's incompleteness theorem).

Your grade for the course will be as follows:

• 15% - Homework
• 40% - Two Midterm Exams
• 45% - Final Exam

There will be two midterm exam and one final exam. The final may be cumulative, covering material from the entire semester. The exam schedule is as follows:

• First Midterm Exam: October 22
• Second Midterm Exam: November 19
• Final Exam: December 17

Follow this link for a Description of Homework requirements.

It is essential not to fall behind, because each lecture is based on previous work. If you have trouble with some material, seek help in the following ways:

• ASK ME! (either in class or privately),
• One of the very best resources may be your fellow students!