Good book on mathematical logic

[haki]

What are your recommedations, all I could find in the local library is Introduction to Mathematical Logic by Mendelson, it is dated 1963, is that still ok? Is there any more state-of-the-art book on mathematical logic? I am interested in self-learning of mathematical logic. I would like to know a good source from where to study.

One more thing, I noticed that prepositional calculus is in ways similar to boolean algebra, is there a formal relation between the two? Since I know from Digital Logic (and,or,xor, Karnough maps, Quinne-McCluskey method,...) some things in prepositional calculus are virtually the same as in boolean algebra. If there are soo similar why invent two systems, that would be like inventing n-tuple therory but as I recall the Set theory was reused to be used with n-tuples aswell, soo I would expect that there would be just prepositional caluclus or just boolean algebra but not both, but then again I am not good at Maths, just started to learn logic.

 

[CRGreathouse]

Enderton's A Mathematical Introduction to Logic would be a fine place to start.

 

[haki]

Thanks for the recommendation, I started to read the book but unfortuately it is not my cup of tea, I decided to rather go with discrete mathematics by Rosen it also covers logic, sets and the like.

 

[MathematicalPhysicist]

the books i intend to read on logic are:
introduction to metamathematics by stephen kleene, a course in mathematical logic by moshe machover.
the first book i think is more for the ug student, and the second is more for the graduate student.

 

[chronon]

I've listed a few books on mathematical logic on my website at the bottom of the page Fermat's last theorem and undecidability - useful books

 

[CRGreathouse]

Thanks for the recommendation, I started to read the book but unfortuately it is not my cup of tea, I decided to rather go with discrete mathematics by Rosen it also covers logic, sets and the like.

I have Rosen's number theory book, but not the discrete math one. How is it?

 

[haki]

Unfortunately I have not yet gotten the discrete math book by Rosen. I looked on Amazon to find a suitable book on mathematical logic but they are not my cup of tea, soo I looked for a discrete math book with a bit of engineering touch I think I have found that in the Rosen's book

You can get the table of content here
http://highered.mcgraw-hill.com/classware/ala.do?isbn=0072880082&alaid=ala_586456

And a sample chapter here (for the 6th edition)
http://highered.mcgraw-hill.com/classware/ala.do?isbn=0072880082&alaid=ala_586465

My second choice was Discrete Math by Biggs but from the TOC it looks like the math logic chapter is a bit to short.

Sadly I couldn't find the 6th or the 5th edition of the Rosen's book in the library, only two 4th edition are available but they will not be available for quite some time, soo I was thinking of buying the book, it is a lot of money but then again I value my educaton very much.

 

[MathematicalPhysicist]

i haven't looked at the links but the book by rosen at least by its cover name suggest that it will not cover exclusively logic alone, so your'e looking for an exclusive logic book?

 

[haki]

I am not looking for an exclusive logic book anymore, reason being, tried reading a couple(by Mendelson and then by Enderton), but they turned out to be a bit to dry reading for my taste, therefore I will go for a discrete math book that has a good chapter on logic, chances are that the chapter will cover what I am looking for, namely Predicates and Quantifiers, in a bit more compact way - by compact I mean something that will not spend 12 pages on describing wffs(well formed formulas), 2-3 pages should do the trick of describing wffs.

 

[MathematicalPhysicist]

i would say that even less then 2 pages would do.
usually you take books on mathemtical logic in order to cover topics such as: church's theorem, goedel's theorems,skolem-lowenheim theorem,compactness theorem etc also to cover first order predicate calcs with/without equality, natural deduction systems, and so on.
i suspect that in book called discrete maths you will not cover any of the theorems i listed, but perhaps you will cover natural deduction.

 

[Zelos]

is there any good book explaining more complex integrals and calculus and bra-kets level math aswell?

 

[haki]

I am looking for a lightweight introduction into logic - strong on predicates, quantifiers and laws of logic, and how to prove the laws of logic etc. A pure mathematical logic book might be a bit to heavy but a discrete math book should cover this but there are lots of them, some don't cover logic at all!, some cover it briefly, I am looking for something that will have a deep enough introduction into logic.

 

[haki]

Looks like Rosen's book will have to wait, on second tough, it is a bit to expensive, anyway I have found a book called Discrete Mathematics for New Technology, Second Edition by R. Garnier and J. Taylor in the library, it will do the trick nicely and then I can move on to a bit more heavy stuff.

 

[MathematicalPhysicist]

One more thing, I noticed that prepositional calculus is in ways similar to boolean algebra, is there a formal relation between the two? Since I know from Digital Logic (and,or,xor, Karnough maps, Quinne-McCluskey method,...) some things in prepositional calculus are virtually the same as in boolean algebra. If there are soo similar why invent two systems, that would be like inventing n-tuple therory but as I recall the Set theory was reused to be used with n-tuples aswell, soo I would expect that there would be just prepositional caluclus or just boolean algebra but not both, but then again I am not good at Maths, just started to learn logic.

the boolean algebra is a special case of something called lattice, and there are different kinds of boolean algebras, and the one you are acquianted to is a 2 valued boolean algebra. (0,1).
to be precise a boolean algebra is a distributive lattice with 0 and 1 and for every element there's a complement to it.

 

[haki]

the boolean algebra is a special case of something called lattice, and there are different kinds of boolean algebras, and the one you are acquianted to is a 2 valued boolean algebra. (0,1).
to be precise a boolean algebra is a distributive lattice with 0 and 1 and for every element there's a complement to it.

Interesting soo prepositions are just as well a distributive lattice with T and F and for every element there's a compliment to it? And Boolean Algebra and prepositional logic is namely the same lattice?