Discover Foundational Mathematics: A Guide to Axioms and Set Theory

[archaic]

Hello, I basically want to know more about the founding axioms, set theory and get a grasp of the foundations. Any suggestions?
Doing a quick search, I have found a free ebook by Kenneth Kunen, http://www.math.wisc.edu/~kunen/770.html, does anyone know of it?
Although I would very much prefer freely available (text)books, recommendations of paid ones are also welcome.
Thank you very much!

 

[jedishrfu]

At what level undergrad or graduate?

For undergrad there's Keith Devlin's book:

https://www.amazon.com/dp/0387940944/?tag=pfamazon01-20

on teaching Set Theory:

https://mathoverflow.net/questions/118254/usage-of-set-theory-in-undergraduate-studies

 

[archaic]

At what level undergrad or graduate?

For undergrad there's Keith Devlin's book:

https://www.amazon.com/dp/0387940944/?tag=pfamazon01-20

on teaching Set Theory:

https://mathoverflow.net/questions/118254/usage-of-set-theory-in-undergraduate-studies

I'm an undergraduate, but I'm looking for something to self-study.

 

[jedishrfu]

There are several online courses like MIT OCW and I found this one from Eliademy:

https://eliademy.com/catalog/fundamentals-of-classical-set-theory.html
But I have not taken it and can’t say how good it is. The description mentions the instructors background and experience which pretty good. It looks to be an undergrad course without mathematical rigor, taught informally and there is a list of related courses at the bottom of the page to consider. Also it mentions its free to take although I don’t know if there are any catches later on.

 

[jedishrfu]

One student on quota mentioned his instructors course and provided a website

https://www.quora.com/What-is-the-best-online-source-for-set-Theory
You could check it out as it looks pretty comprehensive.

@fresh_42 or @Mark44 might have better references.

 

[fresh_42]

You could check it out as it looks pretty comprehensive.

It's on the website of a major British university, so you can't go wrong here. Whether it matches expectations is another question, but this is true for every lecture - some teaching styles fit better than others.

I'm an undergraduate, but I'm looking for something to self-study.

I once bought a book about a completely different topic, only to read the proofs of the various equivalent formulations of AC. Not a bad investment, as it turned out to be the best book about analysis I have, although not easy stuff.

My other encounters with set theory are constraint to a small paperback which dealt with the matter in an easy way, talking about the absurdities it creates and was more meant to be entertaining. A scientific approach probably leads to logic. I consider set theory as a part of logic, rather than a subject on its own. Logic, however, is a complicated area and dry as dust. Thus a qualified answer depends on your definition of "study". Personally, I would prefer a historic approach: Zermelo, Cantor, Russell, Gödel. I once found an original from Russell on the internet and, well, it was basically unreadable. The notation alone would have taken a month to learn. Hence my question what you meant by study, i.e. what for?

 

[archaic]

mathematical rigor

I am actually looking for something rigorous. Maybe I should add that to the topic? I thought that it went without saying that the building blocks should be introduced with adequate rigor. Thank you very much for the recommendations thus far!

Hence my question what you meant by study, i.e. what for?

Enjoyment, pretty much, and to satisfy some curiosity.