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?

Here are a few suggestions (which depending on your background may be more or less useful):
I hope these (admittedly biased) suggestions are some use! 


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 moredepth 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. 


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:



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? 


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). 


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. 

