Good Mathematical Logic Textbook?

FluffyLlamas

I've been trying to decide on a mathematical logic textbook to teach myself a bit. I'm taking a course on it next semester, but I have never had a logic course before (I've had some CS courses though and proof-y math courses). I'm also taking a modal logic course the semester after math logic, so I was wondering if there was a good mathematical logic textbook I could use to review over the summer that perhaps has some relevant material to philosophical logic as well? I know the course I'm taking has no textbook, but rather a collection of notes from the professor. The course notes from two years ago has the following textbooks listed as potential supplementary sources:

Computability and Logic
D. E. Cohen, Ellis Horwood Limited, 1987

Mathematical Logic
E. B. Ebbinghaus, J. Flum, and W. Thomas, Springer-Verlag, 1984

Principles of Mathematical Logic
D. Hilbert and W. Ackermann, Chelsea, 1950

Notes on Logic and Set Theory
S. C. Kleene, Van Nostrand, 1952

A Course in Mathematical Logic
Yu. I. Manin, Springer-Verlag, 1977

Introduction to Mathematical Logic
Elliott Mendelson, Chapman and Hall/CRC, 1997

I've read through reviews for all of them and such and I'm thinking that Ebbinghaus et al or Mendelson would be the best for me?

Thanks for any help!

wisvuze

In order: yes,yes,no , no ,yes yes.
All the "yes" books are more or less on the same intro level to mathematical logic, except I believe the Cohen book is not as advanced as Ebbinghaus or Mendelson ( these two are really good )

The Kleene book isn't a really introductory book, as it presupposes knowledge of model theory.

I wouldn't really bother with the David Hilbert book. I would have to say that it is.. outdated ( especially since this book was written before Tarski was around )

tcbh

Have you looked at Enderton's book on Mathematical Logic? I haven't read that one myself, but it seems to be widely used, and I really liked his book on Computability Theory.