Math Logic Book (Introduction Prop)

[Galadirith]

Hi guys, I have searched the forums but I dont think what I really would like to ask is covered :D. I would really like to find a book for self study on introductory Mathematical Logic, im not really looking for anything covering Sets Or Number thoery (unless of course the text is really really good :D) but really just want to learn the real basics, first-order, propositional.

I ve just finished my A-Levels (so I think that equivical to highschool in the US) and very happy and competent with my maths, so it doesnt need to be for an person with no knowledge of maths, that said Im not at Uni atm, and oviously havnt started and havnt ever taken a logci class as I have never had it avilable to me :D

I had found this book suggested Mathematical Logic by Kleene, I had a look at the content page and it actally seems pretty good what I would want, I think part I would be all that I would read for now, but in time read the rest. I had seen other text going in to more depth + sets etc but atm Im really not looking for anything incredible heavy. I would love it to have some exercises as well to practise my new found skills :D, but its not an absolute must, pehpas theres even a dedicated exercise book for propositional/first-order logic that someone can sugest.

I would really appreciate anyone oppinions as I allway value the voices of PF :D thanks guys

[JustSam]

I suggest "Language, Proof, and Logic" by Jon Barwise and John Etchemendy.

[Galadirith]

Thanks so much for the suggestion JustSam, Ill give that a go :D

[Reedeegi]

I would suggest Donald Kalish's "Logic: Techniques of Formal Reasoning." This text, for myself, taught me not only the fundamentals of first-order logic (including propositional calculus with quantifiers and descriptives, first-order proof and automated proof procedures) but also teaches one to prove theorems formally and rigorously. It serves as a fantastic introduction to formal mathematics, axiomatic logic, and philosophical reasoning.