Is reading Jech's text on Set Theory too little, just enough, or overkill to prepare oneself to do independent research in set theory? This would be my first attempt at doing independent research after taking 5 graduate level math courses and doing well. If I think I'm interested in Set Theory, and want to get a feel for research, is this the way to proceed?
I believe that Jech's book is a solid part of any graduate student's preparation for independent research in set theory. He covers most or even all of the main topics of set-theoretic research, and he does so at quite a high level, including some extremely advanced material. For further study of large cardinals, however, the book should probably be supplemented by Kanamori's book The Higher Infinite (see my review), and for learning forcing, I always encourage my graduate students to read both Jech and also Kunen's book, as well as some others, especially Bell's book on forcing via Boolean-valued models (and my own article on the Boolean ultrapower), and to play all these texts off of one another, as each has some strengths the others lack.
Jech's book is extremely thorough, and I suppose that if you mastered every last bit of it, then indeed I think it would position you for independent research in set theory. But of course, the more typical pattern is to read at first only the easier parts of it, while also learning from other books, and gradually bring oneself to the research level that way.
During and after your study of Jech, you will need someone to guide you to research topics and problems, to suggest problems or areas that might be fruitful for your independent work or which may interest you.
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