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I'm a recent graduate and will likely be out of the maths business for now - but there are a few things that I'd still really like to learn about - forcing and large cardinals being two of them.

My background is what one would probably call a 'first graduate course' in logic and set theory (some intro to ZFC, ordinals, cardinals, and computability theory). Can you recommend any books or online lecture notes which are accessible to someone with my previous knowledge?

Thanks a lot!

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Have you seen "A Beginner's Guide to Forcing" by T. Y. Chow? –  MJD Jul 15 '12 at 4:36
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You may be able to attend this. Two courses about forcing and large cardinals aimed for the non-experts. –  Asaf Karagila Jul 15 '12 at 15:27
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Another interesting set of lecture notes come from a UCLA Summer Logic School covering forcing and independence, found here: math.ucla.edu/~justinpa/class/Forcing.html –  Francis Adams Jul 15 '12 at 17:23
    
Mark Dominus, I printed that this morning and am reading through it right now! Asaf Karagila, pretty much the other side of the planet unfortunately, but thanks for the link. Francis Adams, those look great, thank you! –  us2012 Jul 16 '12 at 3:05

2 Answers 2

up vote 6 down vote accepted

Kunen's "Set Theory: An Introduction to Independence Proofs" is a really well written introduction to, well, independence proofs. It doesn't do a lot with large cardinals, at least not the really large ones, but it does do a thorough treatment of forcing. It also develops Godel's constructible universe in proving the consistency of AC and GCH with ZF, along with other basic methods used in proofs of independence or consistency. I think it finds a good balance between being a gentle introduction, but also efficiently getting through the material. I would highly recommend it for a second set theory course.

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Thank you! Just checked it on amazon: The table of content looks really great. It is unfortunately very expensive though... one of those things I never thought about while I was still at uni and had unlimited access to libraries... –  us2012 Jul 15 '12 at 2:23
    
@us2012 Here it is online: logic.wikischolars.columbia.edu/file/view/… –  Francis Adams Jul 15 '12 at 2:27
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@us2012 Kunen has a new book Set Theory which according to the preface "is a total rewrite of the author's Set Theory: an Introduction to Independence Proofs, first published in 1980". This one is about 20-30 dollars. –  William Jul 15 '12 at 4:20

I would recommend the following as excellent graduate level introductions to set theory, including forcing and large cardinals.

I typically recommend to my graduate students, who often focus on both forcing and large cardinals, that they should read both Jech and Kunen (mentioned in Francis Adams answer) and play these two books off against one another. For numerous topics, Jech will have a high-level explanation that is informative when trying to understand the underlying idea, and Kunen will have a greater level of notational detail that helps one understand the particulars. Meanwhile, Kanamori's book is a great exploration of the large cardinal hierarchy.

I would also recommend posting (and answering) questions on forcing and large cardinals here and also on mathoverflow. Probably most forcing questions belong on mathoverflow.

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Thank you. High-level explanations are just what I'm looking for. Your link for Jech's book points to a program for a conference though, is that intentional? Also, I'm unsure about asking things on mathoverflow - as I'm no longer a student and have no access to other students or advisors in real life, I fear that the questions I might have would be too trivial or unpolished to warrant being asked on MO. –  us2012 Jul 15 '12 at 3:06
    
Thanks, I have edited to correct that link to Jech's book. –  JDH Jul 15 '12 at 3:17
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I see that your review of Kanamori's book is now publicly accessible - awesome! –  us2012 Jul 15 '12 at 15:26

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