Reading materials for mathematical logic Hi everyone, the summer break is coming and I am thinking of reading something about mathematical logic. Could anyone please give me some reading materials on this subject?
 A: Joe Mileti wrote a really nice set of course notes on mathematical logic (approx 20 weeks of lectures). It's a draft for a book titled, I think, "Mathematical Logic for Mathematicians."  The course notes are beautifully written (and beautifully delivered, if you've had the chance to see him lecture).  He's a very nice guy, and I would suggest contacting him about it.  
My memory is a bit hazy about the topics he covered, but we discussed propositional and first order logic, nonstandard analysis, and axiomatic set theory.  I also remember that some highlights included connections to graph theory and algebra (I guess this sort of touches upon his research themes).
A: Here are a few suggestions (which depending on your background may be more or less useful):


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*Logic and Structure by Dirk van Dalen.  I have used this as a textbook when teaching mathematical logic and for that purpose it is decent.  Some people find it a bit dry, but at least it covers a large amount of material in a reasonably clear manner.

*Mathematical Logic by Joseph R. Shoenfield.  This book is, I think, regarded by many logicians as being the gold standard text on the subject.

*A Course in Mathematical Logic by John Bell and Moshe Machover.  This is my personal favorite textbook in mathematical logic.  (Unfortunately, it's a North Holland book and so is a bit less affordable.)

*A Course in Mathematical Logic for Mathematicians by Yuri I. Manin (with contributions from Boris Zilber).  I think that pretty much anything written by Manin is worth taking seriously and this book is no exception.

*Notes on Logic and Set Theory by Peter T. Johnstone.  This is a delightful little (literally) book on logic which is highly recommended (perhaps in conjunction with one of the other larger books from this list).

*The Mathematics of Metamathematics by Helena Rasiowa and Roman Sikorski.  This is a nice book which gives a lattice theoretic development of mathematical logic.  (Difficult to find, but worth a look if your library has a copy.)

*Introduction to Metamathematics by Stephen C. Kleene.  A classic text in mathematical logic which is still a rewarding read.


I hope these (admittedly biased) suggestions are some use!
A: I'm surprised my favorite introduction to mathematical logic hasn't been mentioned by anyone. It's Robert S.Wolf's A Tour Through Mathematical Logic. Wolf has written a book that is extremely compelling to read. His passion for the subject comes through in every sentence. It reads like a novel on mathematial logic and set theory, complete with detailed historical notes, philosophical insights and lots of problems. The book is practically a meditation on the answer to any frustrated student of logic's question,"Why is this important?" I wholeheartedly recommend it as your starting point before you look at any of the more-depth treatments recommended below. As a follow up, I recommend the classic introduction by my old teacher, Elliott Mendelson, An Introduction To Mathematical Logic, a deep and masterfully written introduction for graduate students. Those would be my recommendations. 
A: Set Theory and Logic Robert R. Stoll .
This was our text in some course. See inside. And check your library and/ask the course instructors or try to find any senior students' course outline or  better yet check good univ's websites on such a course. 
A: This book is a general textbook on Logic, so it's not for beginners, but anyway, the text is called "Mathematical Logic" by Yu.Ershov and E.A. Palyutin. Sorry I couldn't find a relevant link anywhere. Maybe it's available in some library somewhere?
A: If you're a beginner to mathematical logic, as you seem to imply, I would strongly recommend you start off by getting acquainted with classical propositional and predicate logic. There is a very useful online set of aritlces on the subject, with interactive exercises. The sections relevant to mathematical logic would be:


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*Logic

*Predicate Logic

*Set Theory

*Recursion

