Which texts to study mathematical logic, for subsequently studying Godel's incompleteness theorems? I want to study Godel's incompleteness theorems and I look for a text which provide mathematical logic with a nice way to make me able to study Godel's incompleteness theorems 
I didn't study mathematical logic before. some people recommended Rene Cori and Daniel lascar text. what do you think ? 
 A: I would like to recommend A First Course in Logic: An Introduction to Model Theory, Proof Theory, Computability, and Complexity. I am in a similar position as yourself, though probably a week ahead, as in without a prior background in symbolic Logic but curious to learn Godel's incompleteness theorem's. I started with this book last week. I am finding it to be a rigrous and pleasurable exposition.
A: Well, how can I resist? My Introduction to Gödel's Theorems (CUP, 2007; second edition forthcoming in March 2013) was written precisely for those with little prior background in mathematical logic, and aims to be very accessible while actually giving the main proofs in quite a bit of detail.
Other options that range a bit more widely into logic and the theory of computation include George Boolos and Richard C. Jeffrey, Computability and Logic (CUP, 3rd edn 1989: there are expanded later editions with John Burgess as a third author, but these are arguably less elegantly done). Richard L. Epstein and Walter Carnielli’s very nice Computability also discusses
computation in general before covering the incompleteness theorems; this
is attractively written with a lot of interesting historical asides.
A: This is not a complete answer, but: If you are just getting started and you are particularly interested in Gödel's Theorems, then I can recommend Gödel's Proof by Nagel and Newman as a gentle introduction. The nice thing about this book is that it is relatively short and not too technical.
A: I learned logic from "Mathematical Logic," by Kleene. It starts from the basics and then goes into Godel's theorems. It's a very solid book, with plenty of examples. 
