21-229 Set Theory I
Rami Grossberg (rami@cmu.edu)
MWF 10:30

12 Units

Purpose: The intention of this course is to introduce the basic concepts and facts of set theory. Set theory was invented about 125 years ago by George Cantor, as an instrument to understand infinite objects. Since than set theory appears to play an important role in several branches of modern mathematics, and serves as a foundation of mathematics.

Contents: Relations and functions, the axioms of Zermelo Fraenkel set theory, basic properties of natural numbers, Peano Axioms, countable and uncountable sets, construction of the real numbers, some basic facts about the topology of the real line (among them characterizing the isomorphism type of the reals as an ordered set, perfect sets, and the Cantor-Bendixson derivative), cardinal numbers and cardinal arithmetic, the continuum hypothesis, well-ordered sets, ordinal numbers and transfinite induction, the axiom of choice, Zorn's lemma. If time permits will discuss some of the following topics: Infinitary combinatorics, filters and large cardinals, Borel and analytic sets of reals.

Level: The course will begin at an elementary level, the only prerequisite is 21-127 (Intro. to modern math), or instructor's permission.

Text: "Introduction to set theory" by K. Hrbacek and T. Jech. Published by Marcel Dekker Inc.

Office Hours: W 2:30-3:30PM or by appointment or whenever else you can find me and I'm not too busy.

Extended office hours: On May 3rd and 5th (M and W) I will have office hours from 2PM to 4PM.

Test Dates: The first midterm will be on Monday 2/22 (instead of a scheduled lecture). The date of the second midterm will be announced.

Evaluation: There will be two one hour tests (in class), weekly assignments, and a three hour final. The final will cover all the course material. These will be weighted as follows:

• Each of the two midterm tests will make up 20% of the grade
• The final will make up 40% of the grade
• Homework assignments will make up 20% of the grade.
Set Theory homework.