Elements of Set Theory

The course covers topics such as the construction of real numbers, the basic theory of transfinite ordinal and cardinal numbers, and equivalent forms of the axiom of choice. Time permitting we will cover also some theorems in set-theoretic topology like Cantor-Bendixson and the Baire Category theorem.

• Lecturer: Ph.D. Juliette Kennedy.
• Schedule: Mondays and Thursdays at 12-14 during fall term 2003. First lecture on Sept 11th, 2003.
• Location: P722
• Two hours examples classes per week. Time and place to be announced.
• Office hours, Mondays 14:00-15:00.
• Book: H. Enderton: Elements of set theory (Academic Press) (Errata)

Bulletins

• PROJECTS TO BE GIVEN THIS MONDAY FEBRUARY 9TH FROM 14:00-16:00 IN P720.

• THE FINAL EXAM FOR THOSE WHO HAVE NOT TAKEN IT WILL TAKE PLACE ON JANUARY 28TH AT 16:00 IN ROOM SI. Projects are to be presented Wednesday, February 4th in SIV, 16:00-18:00.

• Those students who have not taken the final exam yet but who wish to participate in the Reading Seminar on Husserl scheduled for Wednesday, January 28th from 16:00-18:00 are welcome to take the set theory exam at any convenient time between January 29th and February 4rth.

Homeworks

All problems are from Enderton's book.

• Homework 1: p.9, 5-7. p. 33, 26-35
• Homework 2: In Chapter 3, problems 16, 18, 20, 26, 31 and prove theorem 3L.
• Homework 3: In Chapter 3, problems 48, 49, 52. Also prove: For any relation R, the image of A is a set, where A=dom(R). (You need to show that domR is a set.) And in chapter 4, problems: 2, 3, 5, 6.
• Homework 4: Prove associativity of addition for natural numbers. Prove the multiplication we defined is commutative. Do: p. 88, 18, 19, 23, 25, 26, 39, 40.
• Homework 5: p. 101: 1-6. p. 111: 10, 11, 14
• Homework 6: p. 120: 15, 16, 19, 21. p. 133: 2, 4, 5
• Homework 7: p.138: 8, p.144: 10, 11, p.158: 18, p. 161: 29, p. 165: 32, 34.
• Homework 8: p.178, 4-7. p. 184, 11. p.187, 13. These are due November 13.
• Homework 9: p.194, 16-20.
• Homework 10: p.199, 22-25.
• Homework 11: p.207, 26-28, 34, 35, 37.
• Homework 12: p.215: 1,2. p.219: 3,4,5,7,8. p.227: 18,19. Prove: The successor operation (on ordinals) is not normal. Is the operation alpha --> 2alpha normal?