Hi! 


What text on both incompleteness theorems you would recommend for beginner?
Specifically, I'm looking for the text with the following properties:


1) The proofs should be finitistic, in Godel's tradition, i. e. formalizing "I'm unprovable" (not, for instance, via formalization of halting problem);


2) The text must be of reasonable length but with complete proofs, so that one can study them in a reasonable amount of time (e. g. only those forms of recursion theory theorems are proved which are precisely needed for incompleteness proofs);


3) The entire text should be motivated and discussing ideas (even those of philosophical character) before and between technical constructions. 


I would be very thankful if you'll equip your suggestion with some short resume.



The best text to study both incompleteness theorems
First chapter of Jean-Yves Girard, "Proof Theory and Logical Complexity", Vol I, Bibliopolis, 1987


It satisfies all of your conditions, but it is not an elementary book. If I remember correctly, the authors (A.S. Troelstra and H. Schwichtenberg) of the book "Basic Proof Theory" which is published in 2001 wrote in their introduction that their intention was to fill the gap between this and all other (introductionary) books in proof theory. As far as I know, he never published the second volume.


