Description
Book SynopsisThis 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. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
Trade Review“This newest edition has been reclassified, fittingly, as a graduate text, and it is admirably suited to that role. … Those who are already well-versed in logic will find this text to be a valuable reference and a strong resource for teaching at the graduate level, while those who are new to the field will come to know not only how mathematical logic is studied but also, perhaps more importantly, why.” (Stephen Walk, MAA Reviews, January 6, 2023)
Table of ContentsA.- 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.
