Edition: 2nd 1994 (Revised)
List price: $79.95
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Description: This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most striking results are contained in Goedel's work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraiss's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $79.95
Copyright year: 1994
Publication date: 11/15/1996
Size: 6.75" wide x 9.75" long x 1.00" tall
|Syntax of First-Order Languages|
|Semantics of first-Order Languages|
|A Sequent Calculus|
|The Completeness Theorem|
|The Lowenheim-Skolem and the Compactness Theorem|
|The Scope of First-Order Logic|
|Syntactic Interpretations and Normal Forms|
|Extensions of First-Order Logic|
|Limitations of the Formal Method|
|Free Models and Logic Programming|
|An Algebraic Characterization of Elementary Equivalence|