Kunen "Set Theory" 2011 versus 1980 edition - worth buying again?

Question

What are the differences between the original edition (1980) of Kunen's famous book and the new edition (2011)?

Is the updated version worth buying?

(I hope this kind of question is allowed here. I could not find a definitive answer in the guide.)

Addendum: I know the 1980 edition very well.

Answer 1

The presentation differs significantly. The new book actually uses model theoretic tools a lot; for example definability is in terms of the model theoretic approach as opposed to the approach in the old edition with diagonals and projection etc. It also has much less in the way of exercises, so if you want to teach yourself set theory the second edition is probably better as he has put carefully selected problems as opposed to pretty much any and everything as in the first edition.

I learned a lot of set theory from the second edition and the only time I found the first book better is with relation to the proofs of the truth and definability lemmas. That was the only time I used the first book.

The reason that he doesn't cover basic set theory as @Arthur said is because he does the same material in much greater detail in his new introductory mathematical logic text.

With regards to proper forcing, he doesn't really cover it in that much depth, so probably Jech or any other is better.

BTW, the new edition costs less than $25, so you might get one just for the heck of it.

Answer 2

I am taking a course in set theory this semester, following the old edition. Our lecturer was made aware of the new edition only recently, and read it. His verdict was that as an introduction to set theory, the old edition was better, as the new edition only skims over the introductory stuff, more akin to a reminder than an actual introduction.

That being said, if you plan on taking set theory further, the new edition is much more up-to-date on new developments (and which of the old developments turned out to be important). So which one to buy depends on how deep you want to go into set theory.

I apologize for not being more specific here, but as I said, I'm taking the course right now, and I'm nowhere near a personal understanding of the differences.