# Is there really anything wrong with Bourbaki's Set Theory?

Recently I have started reading Bourbaki's Theory of Sets on my own. Regarding one of the explanations of a concept when I went to a Professor of our college, he asked me why I was wasting my time reading a book which contains so many pitfalls. Besides, he also told me that Bourbaki's treatment of Set Theory is wrong. When I asked him about examples, he told me that he thought I would be able to find it myself.

Now this is something that is highly contradicting because here in D. Miller's answer I found that,

...Bourbaki is very far from being suitable for everyone. That said, if you're looking for a reference that's axiomatic, super-abstract, and works in greatest possible generality, and is also crystal clear and careful, Bourbaki is the place to go. ...

And this contradicts the expression I got from my professor. Besides, I himself wasn't able to find out any 'pitfall' in the book so far.

Is there really anything wrong with Bourbaki's Set Theory?

Update

Though Asaf Karagila was very patient with me and answered all my queries, I will be very glad if someone who has gone through Bourbaki's Theory of Sets answers it in detail.

• I find anything by Bourbaki very rigorous, almost to a fault. I know a lot of mathematicians who are put off by the Bourbaki method. However, before Bourbaki mathematics could be said to be in a crisis. That said, I think if this is your first endeavor into set theory, maybe a more modern account would be more appropriate. – Rachmaninoff Nov 23 '14 at 12:02
• I suppose he doesn't mean "wrong" in the sense of "contains false statements as proclaimed 'theorems'" or "contains invalid proofs", but rather "is not the right book to learn se ttheory from, just as Russel-Whitehead's Principia Mathematica are not the right place to learn $2+2=4$ from" – Hagen von Eitzen Nov 23 '14 at 12:10
• Note that none of the members of Bourbaki was a set theorist. And that the developments in axiomatic set theory since the 1960's make pretty much any book about axiomatic set theory written before 1970 obsolete. If you are looking for a rigorous approach, pick up Kunen's 1983 "Set Theory", or Halbeisen's "Combinatorial Set Theory" (which also has a free edition on the author's website). Those do a very good job in presenting modern axiomatic set theory. – Asaf Karagila Nov 23 '14 at 12:41
• Maybe this might be an interesting read? – Dejan Govc Nov 23 '14 at 12:49
• I didn't write anything about it being wrong or not. I didn't read the book past the first couple of pages that seemed overly complicated to me (even if you want to be strictly formal about set theory). You explained that you chose Bourbaki as a candidate because you wanted an axiomatic "super abstract" book about set theory. I'm not sure what "super abstract" would be. But regardless to that, modern axiomatic set theory has changed its characteristics since the 1960s making the book obsolete regardless to any mistakes. – Asaf Karagila Nov 23 '14 at 14:27