Kenneth Kunen Set theory, Studies in Logic (London), 34. College Publications, London, 2011. viii+401 pp. ISBN: 978-1-84890-050-9.
We will certainly follow it in the first part of the course. Later on we might switch to other reading material, which will be announced on this website.
In addition to the obligatory reading material, I will often post supplementary material, dealing e.g. with philosophical or historical issues not covered by the standard material, alternative explanations which might help understanding certain concepts, or some other additions making the course more fun.
Format: This is a reading course, which means that the students are expected to read a certain section of the material every week. The weekly meetings consist of two blocks of 45 min., with a short (~5 min.) break. Generally, I will use the first block to "lecture" and the second to discuss questions from student, do practice exercises etc. In the "lectures", I will present a summary of the material the students had to read, distilling the most important concepts and perhaps presenting things in a slightly different way, though not going into all the details (so just following the lectures without the reading is not sufficient to learn the material; the lectures are only of secondary importance). In the second half, I would encourage students to come up with questions, for example about parts of the material they haven't understood, or we will do practice exercises related to the material.
|Meeting||Date & Time||Material to be prepared||Section and Exercises||Supplementary material|
|1||Wednesday 9 October||
|| Paul Cohen, The Discovery of Forcing.
Very insightful and interesting paper (based on a talk) by Paul Cohen, recounting the history of the forcing method and how he "discovered" it.
|2||Wednesday 16 October||
Prove Lemma IV.2.14
|3||Wednesday 23 October||
Exercise (A4), (A5), (A6), (A7), (A8) and (A12)
from Kunen's old book.
| Akihiro Kanamori, Cohen and Set Theory.
Another interesting paper about Cohen and the history of forcing.
|4||Wednesday 30 October||
Challange: try solving Exercise IV.2.47!
| 6-part video recording of a talk by Paul Cohen, right here in Vienna, in 2006.
(Put the volume up!)
|5||Wednesday 6 November||
|6||Wednesday 13 November||
|7||Wednesday 20 November||
Prove Lemma V.3.12
| Timothy Y. Chow, A beginner's guide to forcing.
A nice article attempting to present the "intuition" behind forcing, written by a non-logician, primarily for non-logicians, and offering some interesting insights. Section 6 of this paper uses the "Booelan-valued models" approach, which we haven't covered (it is explained on p. 275-278 in Kunen), but you can easily read the rest of the paper.
|8||Wednesday 27 November||
Prove the consistency of κ ≤ add(null) directly, without using MA, for regular κ > ω1
|9||Wednesday 4 December||
Think about proving the consistency of "κ ≤ add(null)", "κ ≤ add(meager)" and "κ ≤ b" directly, without using MA, for regular κ > ω1.
|10||Wednesday 11 December||
(in the definition of C', replace "p forces B in C-dot" by "p forces A in C-dot").
|11||Wednesday 18 December|| ||
We will use these lecture notes by Jörg Brendle.
|| Wilfred Hodges, An Editor Recalls Some Hopeless Papers.
An amusing paper, quite unrelated to anything we are doing in this course, but still fun.
|12||Wednesday 8 January|| |
|13||Wednesday 15 January|| ||
For the rest of the course, we will use the textbook Akihiro Kanamori, The Higher Infinite.
Chapter 3 (Sections 10 - 15) availble for download here.
|14||Wednesday 21 January|| ||
We will also need § 0 of Kanamori
Remark: you can replace "L(R)" by "HODR".
Final Exam: there will be 20-30 min. individual oral exam. The purpose of the oral exam is to check how much of the material was understood. The focus will be on understanding the concepts and main ideas in the proofs, but not every single detail. For example, if I ask about the proof of the consistency of MA, you should know how iterated forcing is used in the proof, the bookkeeping argument, the use of the finite support etc., but you don't have to be able to reproduce the entire proof during the exam. I will also not ask for things like the technical definition of ||-*, or some very technical proofs related to products and iterations. Also, certain topics that were not covered particularly well during the course or were a bit too hard, are excluded from the exam. Below is an indication of the material to be prepared.
Material for the exam: