Mathematical Logic

This careful, self-contained introduction to first-order logic includes an exposition of certain topics not usually found in introductory texts (such as Trachtenbrot's undecidability theorem, Fraisse's characterization of elementary equivalence, and Lindström's theorem on the maximality of first-order logic). The presentation is detailed and systematic without being long-winded or tedious. The role of first-order logic in the foundations of mathematics is worked out clearly, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. Many exercises accompany the text.

Inhalt
Contents: Introduction.- Syntax of First-Order Languages.- Semantics of First-Order Languages.- A Sequent Calculus.- The Completeness Theorem.- The Löwenheim-Skolem Theorem and the Compactness Theorem.- The Scope of First-Order Logic.- Appendix. - Extensions of First-Order Logic.- Limitations of the Formal Method.- An Algebraic Characterization of Elementary Equivalence.- Characterizing First-Order Logic.- References.- Index of Notation.- Subject Index.