Introduction to mathematical logic. - Mendelson, Elliot (The Wadsworth & Brooks/Cole mathematics series, 1987)
This is a compact introduction to some of the principal topics of mathematical logic. In the belief that beginners should be exposed to the easiest and most natural proofs, I have used free-swinging set theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as non-constructive set theory was called by Hilbert), at least we should know what we are missing.