Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of logic.This revised edition contains also, besides many new exercises, a new chapter on semantic paradoxes. These informal aspects are kept clearly apart from the technical ones. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers.An overview of the history of logic precedes the main text, while informal analogies precede introduction of most central concepts. The simplicity of syntactic constructions and rules - of a high, though often neglected, pedagogical value - aids students in approaching more complex semantic issues.

The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts.Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. Excellent as a course text, the book presupposes only elementary background and can be used also for self-study by more ambitious students.Starting with the basics of set theory, induction and computability, it covers propositional and first order logic - their syntax, reasoning systems and semantics. This is a systematic and well-paced introduction to mathematical logic.

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