What Are the Best Books to Learn Set Theory from Beginner to Advanced?

[sidkap]

HI friend ,

I am confused about how to start set theory , i want to learn it fully, so please help me in choosing books on this topic which covers from very basics to full advance.

thanks
Sid

 

[mathman]

I don't know what books to recommend. However this question should be in the set theory forum. You'll get more responses there.

 

[Redbelly98]

I don't know what books to recommend. However this question should be in the set theory forum. You'll get more responses there.

Agreed. I have moved the thread to "Set Theory, Logic, Probability, Statistics"

 

[micromass]

What mathematics do you already know?? What do you think you will learn in set theory??

Anyways, the book by Hrbacek and Jech is the best introduction to set theory that there exists. But it may need be suited for you, that's why I asked the questions...

 

[sidkap]

i want to do preparation for Ph D computer science entrance.
for that i want to learn it from scratch

 

[discrete*]

As mentioned by micromass, Hrbacek and Jech is about as good as you get. However, I've found that the book is very pricey. There are alternatives. Consider Stoll's Set Theory and Logic. It's excellent. Some of the chapters focus on formal logic, algebra, or the construction of the number line, but he does it in a way that keeps Set Theory front and center. I personally think Stoll's book is a better introduction to the subject, but there's no doubt that Hrbacek and Jech's book is the gold standard. I've heard people really enjoyed Halmos' Naive Set Theory, but in my opinion, it's good for a beginner, but too skimpy for much else.

I'd figure out what you know already, and where you want to go with Set Theory. Each text assumes something different from the reader, and this is important. Then, once you figure out where you are mathematically, choose a book. Good luck. I've found Set Theory to be one of the more rewarding subjects I have studied/am studying.

 

[sponsoredwalk]

Halmos Set Theory created more problems for me than it solved tbh, I've just ordered https://www.amazon.com/dp/0521168481/?tag=pfamazon01-20
because it not only builds all of the prerequisite logic up in the opening chapter (100 pages!)
but because the preface sounds as if it's exactly what I've been looking for & because it
discusses things I've been trying to find out about in the context of set theory. Read the
preface on amazon's preview feature and see how it applies to you, hopefully it's not a
waste :/

edit: Gave the wrong link - fixed now