Looking for a Better Textbook on Set Theory?

[robertjford80]

I don't like Jech's textbook on set theory because he gives these definitions written in this bizarre language and he doesn't restate the definition in colloquial English. That mathematicians feel its unnecessary to give colloquial examples of their definition or examples, in my opinion, is a mistake. I get the feeling that Jech just assumes people already understand set theory. I'm reading Breuer's text on Set Theory now but it is short and I will soon be done with it. Does anyone else know of a good text on set theory.

 

[Erland]

On what level do you want the book to be? Do you only want elementary set theory to apply in other fields of mathematics, or do you want a more fundamantal, axiomatic approach?

If it is the latter, I recommend "Introduction to Axiomatic Set Theory" by Jean-Louis Krivine, from about 1971.

 

[Fredrik]

I was pretty surprised by this statement about the book by Jech and thought that it doesn't describe the book accurately at all...and then I realized that there's a book written by Jech alone, rather than by Hrbacek & Jech. OK, the book by Jech seems to be more formal, so if that's the one you meant, I see your point, and my recommendation is...Hrbacek & Jech.

 

[micromass]

I was pretty surprised by this statement about the book by Jech and thought that it doesn't describe the book accurately at all...and then I realized that there's a book written by Jech alone, rather than by Hrbacek & Jech. OK, the book by Jech seems to be more formal, so if that's the one you meant, I see your point, and my recommendation is...Hrbacek & Jech.

Jech's book really is a very good book. It contains a wealth of information on set theory and is one of my favorites. However, in order to read Jech, you absolutely need to be comfortable with some set theory already, it's not meant to be a beginners book. Hrbacek & Jech is also extremely good and is more suitable to absolute beginners in set theory.

 

[mathwonk]

the first book i read in high school on set theory seemed very nice, by Erich Kamke. Then Halmos' Naive set theory is very popular, and there is always the masterpiece by Hausdorff. I seem to remember that after reading Hausdorff it seemed Kamke was just a repetition of a small part of that book. I also enjoyed browsing in Georg Cantor's book, On contributions to the founding of transfinite numbers, but it is for those who appreciate original sources.

 

[gufiguer]

The book by Enderton is good too.

 

[Luis Gomez]

The book by Enderton is good too.

Indeed