This is a compact mtroduction to some of the pnncipal tOpICS of
mathematical logic . In the belief that beginners should be exposed to
the most natural and easiest 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 nonconstructive set theory was called by
Hilbert), at least we should know what we are missing. The major changes
in this new edition are the following. (1) In Chapter 5, Effective
Computability, Turing-computabIlity IS now the central notion, and
diagrams (flow-charts) are used to construct Turing machines. There are
also treatments of Markov algorithms, Herbrand-Godel-computability,
register machines, and random access machines. Recursion theory is gone
into a little more deeply, including the s-m-n theorem, the recursion
theorem, and Rice's Theorem. (2) The proofs of the Incompleteness
Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and
its connection with Godel's Second Theorem are also studied. (3) In
Chapter 2, Quantification Theory, Henkin's proof of the completeness
theorem has been postponed until the reader has gained more experience
in proof techniques. The exposition of the proof itself has been
improved by breaking it down into smaller pieces and using the notion of
a scapegoat theory. There is also an entirely new section on semantic
trees.