Timeline for Preparing for Set Theory Research
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Jul 29, 2021 at 20:54 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| Jun 26, 2013 at 14:58 | comment | added | Todd Eisworth | Of course, things that took me weeks to figure out on my own were clarified in a few minutes of discussion with Andreas once I got into grad school... | |
| Jun 26, 2013 at 14:36 | comment | added | Todd Eisworth | My own path to set theory involved reading through the green version of Jech's book back in the late 80s. No one at my undergrad did set theory, but I ran across Jech's book in the library and I was hooked. | |
| Jun 25, 2013 at 21:31 | comment | added | Joel David Hamkins | I'm intrigued... | |
| Jun 25, 2013 at 21:08 | comment | added | Andrés E. Caicedo | (I have a plan. Maybe in a year. I'll let you know.) | |
| Jun 25, 2013 at 20:53 | comment | added | Joel David Hamkins | So it seems that probably we are in basic agreement. And yes, let's discuss it further over drinks! | |
| Jun 25, 2013 at 20:46 | comment | added | Andrés E. Caicedo | Of course I agree with the main statement. I disagree that knowing the book thoroughly would allow you to do research nowadays (but I accept there may be exceptions). I agree that Kanamori's book and others would also be essential. Still, I don't think that books are the way to reach the appropriate place. (I also don't know what being a generalist is, but I suspect that is something that would be more interesting to chat about over dinner or a beer.) | |
| Jun 25, 2013 at 20:42 | comment | added | Joel David Hamkins | Andres, are you arguing with my main statement, "Jech's book is a solid part of any graduate student's preparation for independent research in set theory"? Or perhaps you are arguing only with my reluctant admission that if someone mastered every last bit of Jech's book (which never happens), then one would be prepared for research in set theory. If the latter, then I basically agree, which I why my students are also reading Kanamori, etc. as well as research articles, and so on. | |
| Jun 25, 2013 at 20:39 | comment | added | Andrés E. Caicedo | If you say so, Joel. | |
| Jun 25, 2013 at 20:37 | comment | added | Joel David Hamkins | Andres, I would add that you and I probably don't agree 100% on what counts as a "current" topic in set theory, since I find it likely that I may be more of a generalist than you, and to be a generalist takes a different kind of preparation. | |
| Jun 25, 2013 at 20:37 | comment | added | Andrés E. Caicedo | On forcing axioms: The proof of the consistency of $\mathsf{MM}$ leaves out all the difficulties. In fact, the treatment of iterations is much less thorough than in his "Multiple forcing" book. (And in terms of the theory of forcing axioms, the results there are badly outdated.) In the 70s, when it first appeared, Jech's book would have been enough to leave you ready for research. Nowadays, it is impossible to achieve that with a book. Anyway, if we want something that after Jech brings us closer, then the Handbook is the place to go. | |
| Jun 25, 2013 at 20:33 | comment | added | Joel David Hamkins | Yes, it is an introductory graduate text. But meanwhile, I don't know of any introductory course that covers all of Jech. I think to cover it in its entireity would fill three or four semesters at least (but I wouldn't recommend this, since one would want to see more large cardinals and other topics, as you mention, and use other books for that). He does cover quite a bit of forcing axioms (e.g. MA, MM, PFA, etc.) and even some pcf theory and determinacy. He is much less thorough on large cardinals, which is why I find Jech+Kanamori a great combination. | |
| Jun 25, 2013 at 20:32 | comment | added | Asaf Karagila♦ | I agree with Andres, and in particular the proof of the covering lemma on chapter 18 is presented in a way where there is some "minor bits left for the reader", but that's actually the main difficulty of the proof and I felt cheated when I saw the whole proof in class some two years ago and compared it to the proof in Jech. | |
| Jun 25, 2013 at 20:28 | comment | added | Andrés E. Caicedo | But Joel, Jech's is only thorough on introductory material, don't you think? If one wants to learn forcing axioms, or pcf theory, or determinacy, or reflection principles, or just about any current topic, Jech's book only provides a cursory presentation. | |
| Jun 25, 2013 at 20:24 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |