which texts do you recommend to study mathematical logic ?  I intend to study mathematical logic , my purpose is to get to Godel's incompleteness theorems 
I haven't study any mathematical logic before 
so what is the good text which I can use for this purpose ? 
I search for a book give me the right picture , and good explanations 
I will use it as self-study
 A: MR0194311
Lyndon, Roger C.
Notes on logic. 
Van Nostrand Mathematical Studies, No. 6 D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London 1966 vi+97 pp. 
This was by far the best introductory book when I studied logic (also by self-study) back
in 1970-s.
A: I'm a huge fan of Boolos, Burgess, and Jeffreys, "Computability and Logic." The first-order logic part proper starts with the chapter "A precis of first-order logic: syntax," and the book can be begun there without any loss of continuity. (The previous chapters are a lengthy intro to computability theory; I found it helpful to return to those chapters after finishing the chapters on first-order logic.)
Alternatively, Richard Kaye's book "The mathematics of logic" is quite good; it takes you as far as Godel's Completeness Theorems, at which point it's easy to switch to something like Boolos, Burgess, and Jeffreys to cover the incompleteness theorems.
(And, for a nice preview of Godel to give you some motivation, this paper by Rosser (http://philpapers.org/rec/ROSAIE) is a wonderful exposition of the reasoning around Godel's incompleteness theorems, and further results.)
A: I suggest Cori and Lascar's "Mathematical logic", two small books ; the first book covers propositional calculus, Boole algebras and predicate calculus ; the second recursive functions, Gödel's theorems, set theory and the basics of model theory. I found the proofs precise, the examples nice.
