Elements of set theory, fall 2012

Grades will be submitted Wednesday, December 19th. Students can write to me for their exam grades after Tuesday December 18th.

The new date of the FINAL EXAM is November 15 in A111 or B123 at 16-20. (There is a list on the door which tells which room your exam is in.) The exam is based on the homework problems and on the theorems we covered in class. Some of the very long ones, like Lemma 6R, and the Transfinite Recursion Theorem Schema on p. 177, you will not have to prove but you may have to sketch the proof. Remember that there are different proofs of the Schroder-Bernstein Theorem (p.147). Please feel free to contact me if you have any questions.

There will be one more example class on Friday November 2nd, in the usual room and time.

Contents

Axioms and operations, relations and functions, natural numbers, construction of the real numbers, cardinal numbers and the axiom of choice, orderings and ordinals, ordinals and order types, special topics. 

Lecturer

Juliette Kennedy

Scope

10 cu.

Type

Intermediate studies

Prerequisites

No special prerequisites.

Lectures

Weeks 36-42, Monday 10-12 in room C123, Monday 14-16 in room C124, Tuesday 10-12 in roon B120, Tuesday 14-16 in room C124. NOTE THAT THIS IS A ONE PERIOD COURSE.

By Tuesday October 16th we covered up to page 203 of the book. Our final theorem of the week was 7U. In the spring semester we will pick up right at this point, finish Enderton and then go on to Drake's book---large cardinals, ultraproducts etc. 

Exams

Homework:

For the week ending September 4rth: page 33: 23,24, 32.   page 38: 2. page 53: 19. page 55: 31 (we did this in class but think it over again). Finish proof theorem 3A on page 36. Read proof of Recursion Theorem on omega in preparation for our proving it in class this Monday.
For the week ending September 11th: Finish part 3 of the recursion theorem on omega, page 75. page 88: 18,19 (hint: by induction on m for fixed d),23,24,25. page 101: 3,4,5.
For the week ending September 18th: p.101: 5,6,9. p. 111: 10, 14. For the Friday class: p. 120: 15,17, 18,19,21, 22.
Homework for October 3rd: p. 133: 3,4,5. p. 138: 8,9. (Hint for question 8: use induction.) Homework due Friday October 5: p. 144: 10,11. p. 151: 16.

Homework for October 10th: p. 158: 20,21,24. p. 161: 28,29. Homework due Friday October 12: p. 165: 32, 34,35,36.

Homework for October 17th: p. 178: 6,7. p. 184: 10. p. 187: 12, 13. Homework due Friday October 19: p. 194: 16, 17,18,19,20. p. 200: 23,24.

Bibliography

Enderton: Elements of Set Theory, Academic Press.

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Exercise groups