Books on axioms, theorems, and proof methods

[C0nfused]

Book suggestions- Moved in Science book reviews

Hi everybody,
I am looking for books about Logic and Set Theory. In particular, I am looking for not very advanced books. What are axioms, how do theorems connect to the axioms, how are we sure that some methods of proving give always correct and general results-these are some of the questions that I am looking for answers (i think this is part of mathematical logic, isn't it?). Any help would be appreciated
Thanks

P.S: I don't live in the U.S.A or U.K. so as you understand, only really well-known books might be found in my country. So I would prefer you to suggest some of the "classics" that can probably be found everywhere

 

[fourier jr]

'axiomatic set theory' by patrick suppes & 'theory of sets' by kamke is are the best ones. kamke's doesn't have any problems in it though. they're both available from dover, which isn't some obscure publishing company. they'll be cheap books too.

 

[mathwonk]

halmos' naive set theory is also a classic.

you can search here:
http://dogbert.abebooks.com

I found copies in germany, australia, england, and denmark, but for the price of some of them, you could probably afford to order from iowa and pay shipping.

i read some of kamke's book in high school, and enjoyed it as far as i got.

kamke was a dover book even then and hence very cheap.

these are mopre set theory than logic though.

i myself learned about all the logic i have ever needed from principles of mathematics, by allendoerfer and oakley, (in high school).

It was a big advantage to enter college aftyer reading this book. the basic logic stuff in there is not taught to students at the university where i work until junior year, if then. ludicrous.

here is another basic book with some easy logic in it:

Introduction to Modern Algebra
John L. Kelley
Price: US$ 4.49 [Convert Currency]
Book Description: D. Van Nostrand Company, 1960. Trade Paperback. Good. "Official Textbook for the Continental Classroom". Bookseller Inventory #512660

Bookseller: North State Books (Lincolnton, NC, U.S.A.)

 

[C0nfused]

Thanks for your answers