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This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines.

Mathematical Logic

A.- I Introduction.- II Syntax of First-Order Languages.- III Semantics of First-Order Languages.- IV A Sequent Calculus.- V The Completeness Theorem.- VI The Löwenheim-Skolem and the Compactness Theorem.- VII The Scope of First-Order Logic.- VIII Syntactic Interpretations and Normal Forms.- B.- IX Extensions of First-Order Logic.- X Computability and Its Limitations.- XI Free Models and Logic Programming.- XII An Algebraic Characterization of Elementary Equivalence.- XIII Lindström's Theorems.- References.- List of Symbols.- Subject Index.