Overly formal book on mathematical logic.

Question

In the preface to his book on logic Dirk van Dalen talks about the duality between "profane" and "sacred" logic, referring to relaxed logic and extremely formalized logic. He then explains his book will be more of the relaxed kind.

I've read the introduction of a handful of books on logic and this is a common theme, they all say "this can be done very very formally, but we won't do it here". I feel, however, that due to my interest in mathematical philosophy (related to the fact that I'm beginning to study independence proofs) I'm in need of one of these overly formal books on logic that so many authors want to avoid writing.

Can somebody give me a recommendation?

Answer 1

Try Alfred Tarski's Introduction to Logic and to the Methodology of Deductive Sciences. His notation is dated but it's still a good source. And the book is very cheap.

Answer 2

Some suggestions:

• S.W.P. Steen, Mathematical Logic with special reference to the natural numbers (1972)

• J.Donald Monk, Mathematical logic (1976)

• John L. Bell & Moshe Machover, A Course in Mathematical Logic (1977)

• Gaisi Takeuti, Proof Theory (2nd ed - 1987)

• George Tourlakis, Lectures in Logic and Set Theory. Volume 1: Mathematical Logic (2003).