Gödel's Incompleteness Theorem

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(Apologies if I am in the wrong part of the forum)
What branch of mathematics does Gödel's Incompleteness Theorem deal with?(I'm guessing Logic) and does anyone know any good books at the undergraduate level that would help to lay a foundation for understanding his theorem. I am "teaching myself" so the book(s) would need need to be fairly thorough. His theorem seems to be fairly important and my understanding of it is so poor.
Thanks in advance for any and all responses.
 

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Hurkyl
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Gödel's first incompleteness theorem is a theorem of formal logic -- it proves that no mathematical theory can have all four of the following list of properties:
1. Consistency
2. Completeness
3. Capable of fully expressing integer arithmetic
4. A computability condition on the set of axioms


Aside from certain topics in formal logic / computability theory, I believe it's only real use is in philosophy. Alas, it's so often misquoted that it's hard for me to tell if it's really important philosophically, or if it's just that the misquotes sound important.
 

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