This short book geared towards undergraduate students of computer science and mathematics is
specifically designed for a first course in mathematical logic.A proof of Gödel's completeness
theorem and its main consequences is given using Robinson's completeness theorem and Gödel's
compactness theorem for propositional logic. The reader will familiarize himself with many
basic ideas and artifacts of mathematical logic: a non-ambiguous syntax logical equivalence
and consequence relation the Davis-Putnam procedure Tarski semantics Herbrand models the
axioms of identity Skolem normal forms nonstandard models and interestingly enough proofs
and refutations viewed as graphic objects. The mathematical prerequisites are minimal: the book
is accessible to anybody having some familiarity with proofs by induction. Many exercises on
the relationship between natural language and formal proofs make the book also interesting to a
wide range of students of philosophy and linguistics.
