How to Read this Book

So we shall now explain how to read the book. The right way is to

put it on your desk in the day, below your pillow at night, devoting

yourself to the reading, and solving the exercises till you know it by

heart. Unfortunately, I suspect the reader is looking for advice how

not to read, i.e. what to skip, and even better, how to read only some

isolated highlights.

(Saharon Shelah in the introduction to his book "Classification

Theory and the Number of Non-Isomorphic Models")

In mathematics, as anywhere today, it is becoming more difficult to

tell the truth. To be sure, our store of accurate facts is more plentiful

now than it has ever been. ... Unfortunately, telling the truth is not

quite the same as reciting a rosary of facts.

(Gian-Carlo Rota, 1985)

W. A. Hurwitz used to say that in teaching on an elementary level

one must tell the truth, nothing but the truth, but not the whole truth.

(Mark Kac, 1976)

We wrote this text for two kinds of readers: beginning graduate students who

want to get some grounding in set theory, and more advanced mathematicians who

wish to broaden their knowledge of set theory. Furthermore, we wanted this text

to be useful both as a textbook for a regular graduate course, as well as for those

readers who wish to use it without the guidance of an instructor.

Volume I contains the basics of modern set theory. Many graduate texts on

analysis, algebra, topology, or measure theory begin with a review of parts of this

material as "set-theoretic prerequisites." Thus, Volume I is primarily aimed at be-

ginning graduate or advanced undergraduate students. It can be used as a textbook

in an introductory set theory course, or as supplementary reading in a course that

relies heavily on set-theoretic prerequisites. Volume II is aimed at more advanced

graduate students and research mathematicians specializing in fields other than set

theory. It contains short but rigorous introductions to various set-theoretic tech-

niques that have found applications outside of set theory. Although we think of

Volume II as a natural continuation of Volume I, each volume is sufficiently self-

contained to be studied separately. Since our terminology is fairly standard, more

advanced students may be able to skip the first few sections of Volume I or even go

directly to Volume II.

If you do not have the benefit of an instructor who can tell you what to skip, the

best policy is to proceed as follows: Read the Introduction. It will give you some

general idea what we are up to. If you don't understand every word of it, don't

worry. Next, find out at which point of the rest of the book things start to look