A TASTE OF SET THEORY


(Weizmann Institute of Science, Faculty of Mathematics, Second Semester) Mon. 14:00-16:00, Ziskind 1

B. Tsaban

(2 points)

Description: This is an introductory course aimed at students with little or no background in set theory, but with strong intellectual curiosity, in particular concerning infinite entities.

(Students with good background in set theory can also find the course interesting, but may wish to skip the first few lectures -- contact the lecturer for more details on this option.)

Designed to give the student a variety of basic tools that he or she might need in his works in other mathematical disciplines, the aim is to cover a single topic on each of the course's lectures. Several exercises will be handed each week.

The planned topics are:

  1. The axioms of mathematics
  2. Ordinal numbers
  3. Cardinal numbers
  4. Real numbers
  5. The Axiom of Choice and basic cardinal arithmetic
  6. The Axiom of Regularity
  7. Filters, ultrafilters, and Boolean Algebras
  8. Stationary sets
  9. Combinatorial set theory
  10. Measurable cardinals
  11. Borel and Analytic sets
  12. Models of Set theory