What are some recommended books on mathematical logic and set theory?

In summary, the person is looking for books on Logic and Set Theory, and prefers not very advanced books. They are seeking answers to questions about axioms, theorems, and methods of proving. They also mention that they are specifically interested in mathematical logic. They ask for suggestions for "classics" that can be found anywhere, and one person recommends "Discrete Mathematics" by Kenneth Rosen, and another suggests "Language, Proof and Logic" by Jon Barwise and John Etchemendy, which includes interactive software for practice and evaluation.
  • #1
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Hi everybody,
I am looking for books about Logic and Set Theory. In particular, I am looking for not very advanced books. What are axioms, how do theorems connect to the axioms, how are we sure that some methods of proving give always correct and general results-these are some of the questions that I am looking for answers (i think this is part of mathematical logic, isn't it?). Any help would be appreciated
Thanks

P.S: I don't live in the U.S.A or U.K. so as you understand, only really well-known books might be found in my country. So I would prefer you to suggest some of the "classics" that can probably be found everywhere
 
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  • #2
"Discrete Mathematics" from Kenneth Rosen, McGraw Hill, is a classic. It treats logic (along with other topics like number theory, sets, probability, Boolean Algebra, algorithms, etc) in depth, in clear language for beginners, with plenty of examples, exercises and case studies, many of which are drawn from computer science.
 
  • #3
Thanks for your suggestion. I will check it out
 
  • #4
A really great modern introduction to the subject is Language, Proof and Logic by Jon Barwise and John Etchemendy. Not only is the text superb, but it comes with software by which you can formulate arguments. And then you can send your solutions to their website's "Grade Grinder", and they will evaluate them for you!

The homepage (at Stanford) is here:

http://www-csli.stanford.edu/LPL/ [Broken]

Do check it out!
 
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1. What is mathematical logic?

Mathematical logic is a field of mathematics that studies the principles and methods used in reasoning and proving mathematical statements. It uses symbols and rules to analyze the structure of logical arguments and to determine whether a statement is true or false.

2. How are books on mathematical logic helpful?

Books on mathematical logic provide a comprehensive understanding of the foundations of mathematics and the principles of logical reasoning. They also provide techniques for constructing and evaluating mathematical proofs, which are essential for understanding and solving complex mathematical problems.

3. What are the main topics covered in books on mathematical logic?

Books on mathematical logic cover a range of topics including propositional and predicate logic, set theory, proof theory, model theory, and computability theory. They also cover topics such as mathematical induction, axiomatic systems, and the foundations of mathematics.

4. Are books on mathematical logic only for advanced mathematicians?

No, books on mathematical logic are suitable for anyone interested in understanding the principles of logical reasoning and the foundations of mathematics. While some advanced topics may require a strong mathematical background, many introductory books on mathematical logic are accessible to beginners.

5. What are some recommended books on mathematical logic?

Some popular books on mathematical logic include "Mathematical Logic" by Ebbinghaus, Flum, and Thomas, "Introduction to Mathematical Logic" by Elliott Mendelson, and "A Mathematical Introduction to Logic" by Herbert Enderton. It is also recommended to consult with a mathematician or a university course for further recommendations.

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