Axiomatic Set Theory (Spring 2010)


EVALUATION FORMS: Please take a form from the envelope in my pigeon hole in Science park, fill it in and put it back in. This request is due to the fact that they sent the forms after our last lecture.

ALL ASSIGNMENTS HAVE BEEN MARKED. GRADES AVAILABLE FROM THE BLACKBOARD OR FROM ME ON MONDAY 31 OR TUESDAY 1ST OF JUNE.



Year: Spring 2010
The first class will start at 9am on Tuesday February 2, 2010 in room REC-P 0.17.

Participants are advised to obtain the main textbook of the course: The Joy of Sets: Fundamentals of Contemporary Set Theory (Undergraduate Texts in Mathematics) by Keith Devlin.

Lecturer: George Barmpalias
The final grade will be determined by biweekly homework assignments and an optional exam. If you take the optional exam, the grade will be based on the basis of a ratio homework/exam that maximizes your score. The optional exam was going to be on May 28 from 13:00 - 16:00 hrs. in REC-A AB.44. Since I have not received any requests for taking the exam, THE EXAM IS NOT GOING TO TAKE PLACE.

The main text that we will be using is: The Joy of Sets: Fundamentals of Contemporary Set Theory (Undergraduate Texts in Mathematics) by Keith Devlin. Errata


Description: Set theory is a branch of mathematics that studies collections of mathematical objects, i.e. sets. It was initiated by Cantor and Dedekind in the late 19th century and by the very beginning of the 20th century various antinomies (most notably Russell's paradox) showed that naive set theory is inconsistent. This lead to the proposal of various axiomatic systems for the formal development of the theory that avoids the known paradoxes. Of those system the Zermelo-Frankel set theory with the axiom of choice became the most established. This is the set theory that we are going to study in this course. We will discuss the axioms, how various notions from mathematics are formalized in set theory and how we can define a hierarchy of infinities in order to classify the sets according to their size. In particular, ordinal and cardinal arithmetic is a rather central topic in the course. Extra topics include the constructible universe, the Borel hierarchy and a discussion on independence proofs in set theory.


Prerequisites: The only prerequisite is mathematical maturity.
Slides by Jouko Vaanaanen:

Homework:

Problem Sessions: