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I am very new to set theory and have only learned the basics up to cardinal and ordinal aritmetic. I would like to learn about large cardinals and I am reading Thomas Jech's Set Theory. I have read that Kanamori's book is a good resource but I think that one is a bit advanced for me still. Are there any other books out there? Also is there a book that looks at the philosophical aspects of the subject and is less technical? Thanks:)

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You should learn more about basic set theory, then. Kanamori's book is an excellent reference, and for large cardinals I think it's better than Jech's book. I find his writing style to be easier to read. You should continue learning the basics of set theory, when you can read Kanamori's book then you're in a level sufficient for understanding large cardinals. – Asaf Karagila Jul 12 '13 at 14:02
I guess the easiest book on the topic is Set Theory: An Introduction to Large Cardinals by Drake. – Michael Greinecker Jul 12 '13 at 14:16
Though quite nice, the problem with Drake's book is that it is badly dated. In particular, most large cardinals that are the focus of current research are not developed there, notoriously Woodin cardinals. Kanamori is the reference. – Andrés Caicedo Jul 12 '13 at 15:32
For philosophical aspects, I would suggest to begin with Maddy's two papers on "Believing the axioms", J. Symbolic Logic 53 (1988), no. 2, 481-511 and no. 3, 736-764. – Andrés Caicedo Jul 12 '13 at 16:12
"The King's Cardinal" by Peter Gwyn. (Sorry, couldn't resist. I'll get my coat.) – Yemon Choi Jul 13 '13 at 2:03

2 Answers 2

The question got bumped, and so let me take this opportunity to say that Kanamori's book is definitely the right source for anyone who is interested in entering this fascinating subject. Some time ago, I wrote a review of it, which you can find at:

If you find his book to be too advanced, then the solution is simply to learn a little more set theory, which you can do by studying Jech's book Set Theory, among others. Much of Kanamori's book, however, is not so technical, and he has a delightful habit of weaving the historical development into the unfolding story. It is a pleasure to read!

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There's Rucker's Infinity and the Mind (Appendix A in particular), although you may find it a bit basic (plus I don't know if it has been updated since it was written).

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