Well-written undergraduate-level introduction begins with symbolic logic and set theory, followed by presentation of statement calculus and predicate calculus. First-order theories are discussed in some detail, with special emphasis on number theory. After a discussion of truth and models, the completeness theorem is proved. ". . . an excellent text." — Mathematical Reviews. Exercises. Bibliography.
Here's a sample of other books in this Dover category
Introduction to Logic by Alfred Tarski This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.
Set Theory and the Continuum Hypothesis by Paul J. Cohen This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The award-winning author employs intuitive explanations and detailed proofs in this self-contained treatment. 1966 edition. Copyright renewed 1994.
Satan, Cantor and Infinity: Mind-Boggling Puzzles by Raymond M. Smullyan A renowned mathematician tells stories of knights and knaves in an entertaining look at the logical precepts behind infinity, probability, time, and change. Requires a strong background in mathematics. Complete solutions.
