Recently, I got interested in Mathematical Logic and now I am looking for good introductory books on Mathematical Logic for beginners. In fact, I plan to read some good books on Metamathematics also. So, if possible, in your answer mention separately the names of the books which are suitable for a beginner of Mathematical Logic and Metamathematics.
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3Enderton and Kleene each have a book with the word "Introduction" in their title. Enderton's book is more undergraduate level, while Kleene's book is more graduate level. If you master both books, you are well on your way to studying metamathematics, and can choose one or some or all of proof theory, set theory, recursion theory, or other studies in logic and foundations to pursue. – May 18 '15 at 06:22
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Mathemaical logic by Shoenfield contains many parts of mathematical logic, https://books.google.com/books?id=D0k3YgEACAAJ&dq=mathematical+logic+shoenfield&hl=en&sa=X&ei=0aBZVdL-D8WqywPngYHwBg&ved=0CB4Q6AEwAA – Rahman. M May 18 '15 at 08:20
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You may find the tutorial that comes with my proof-checking software to be a useful introduction. Visit my website at http://www.dcproof.com The rules of logic used are a simplified version of standard FOL. They are easier to use and more in line with those implicitly used in mathematics textbooks. – Dan Christensen May 18 '15 at 14:23
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Not really a textbook on the subject, but wonderful nonetheless: Gödel, Escher, Bach by Hofstadter. He discusses formal systems. – Akiva Weinberger Jun 02 '15 at 19:55
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There is a lot of information and guidance linked at the Teach Yourself Logic page. In particular there is a (free!) 100 page Study Guide looking at a selection of the best texts available at different levels, with explanations of what they cover and recommendations for what to read in what order.
Peter Smith
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4If I'd been doing self-promotion if I'd have said "linked at the quite terrifically splendid Teach Yourself Logic page ..." :) – Peter Smith May 18 '15 at 15:12
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In your Appendix there are some references of sections which you have removed later. Please go through the book once more. – May 26 '15 at 03:38
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You may be interested with my work : http://settheory.net, where I tried to provide an optimal exposition of the foundations of maths, starting from scratch and going fast. Of course in this rather small number of pages I could not go as far as usual books but I focused in the core concepts, with a few original aspects.
user27887
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The answer to this question depends on which aspect of logic you want to learn about. If you want to aim at model theory (which might be the case if you like algebra better than computer science), I would recommend the script "Sets, models and proofs" by Moerdijk and van Oosten, available here:
http://www.staff.science.uu.nl/~ooste110/syllabi/setsproofs09.pdf
It contains what I include in a one semester course in logic for mathematicians, is very well written and suitable for self studies.
