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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

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This might help: math.stackexchange.com/questions/205518/… –  Sniper Clown Dec 21 '12 at 1:53
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I think that a high-school student who is not already pretty sophisticated is better off asking at math.stackexchange.com. –  Andy Putman Dec 21 '12 at 2:14
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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.

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does the text provide the complete proof of godel's theorems ?! or just the book mentioned with no proof ? –  Maths Lover Jan 5 '13 at 10:54
    
My real goal is to study the proof of godel's theorems that's what i look for , so if the text don't prove the theorem ! that's not good ! is the text suitable to a high school student ?! –  Maths Lover Jan 5 '13 at 10:56
    
The chapter 6 (1-4 is in book I and 5-8 in book II) is "Formalization of arithmetic, Gödel theorems", and ends with stating and proving the theorems. The proofs are short, but of course use many results detailed before. The books are very progressive and start very low, but since I have no idea what a "high school student" knows, I can't assure you it's a perfect fit. –  Julien Puydt Jan 6 '13 at 10:13
    
I studied geometry ,high school algebra , calculus " very good course " and I study abstract algebra and linear algebra now have general idea of logic ____________ you said " the proof is short but use many results delaited before " do you mean that the proof is not complete ? or you mean that it's complete but he gave a nice proof who is shorter than the traditional one ? –  Maths Lover Jan 6 '13 at 13:27
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I suggest the math part of stackexchange. Take your time. –  Julien Puydt Jan 12 '13 at 9:50
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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.

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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.)

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