Books about the foundations of mathematics

saltkraxen

Hello,

Does anyone know of any good books that covers the foundations of mathematics (i.e. mathematical logic, axiomatic set theory, proof theory, model theory, type theory, recursion theory...)?

Keeping in mind that I'm still in high school. (Although I'm taking math courses at my local university.)

EDIT: Should this be in: "Math & Science Learning Materials"? Mod can move it if he/she thinks so... (This is my first post...)

micromass

For axiomatic set theory, an extremely good introduction is "Introduction to Set theory" by Hrbacek and Jech: http://www.amazon.com/Introduction-E.../dp/0824779150

A good book on mathematical logic is "Mathematical logic" by Ebbinghaus: http://www.amazon.com/Mathematical-L...ds=Ebbingshaus
This may be hard for a beginner though, so check it out before buying.

A good introductory book on logic is "A mathematical introduction to logic" from Enderton: http://www.amazon.com/Mathematical-I...words=Enderton

atyy

I'm in the middle of Robert Wolf's A Tour Through Mathematical Logic. It's so far beautifully written and accessible.

saltkraxen

Thanks for the suggestions!

genericusrnme

Bourbaki's 'Theory of Sets' covers some of that and is quite a nice book to go through.