Mathematical logic
Author(s)
Bibliographic Information
Mathematical logic
（Undergraduate texts in mathematics）
Springer-Verlag, 1996, c1994
2nd ed., corrected second printing
- : us
- : gw
- Other Title
-
Einführung in die mathematisch Logik
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Note
Original edition published: Darmstadt : Wissenshaftliche Buchgesellschaft
Includes bibliographical references (p. [277]-279) and indexes
Description and Table of Contents
- Volume
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: us ISBN 9780387942582
Description
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. It covers several advanced topics not commonly treated in introductory texts, such as Fraisse's characterization of elementary equivalence, Lindstroem's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
Table of Contents
- Preface
- Part A: 1. Introduction
- 2. Syntax of First-Order Languages
- 3. Semantics of first-Order Languages
- 4. A Sequent Calculus
- 5. The Completeness Theorem
- 6. The Lowenheim-Skolem and the Compactness Theorem
- 7. The Scope of First-Order Logic
- 8. Syntactic Interpretations and Normal Forms
- Part B: 9. Extensions of First-Order Logic
- 10. Limitations of the Formal Method
- 11. Free Models and Logic Programming
- 12. An Algebraic Characterization of Elementary Equivalence
- 13. Lindstroem's Theorems
- References
- Symbol Index
- Subject Index
- Volume
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: gw ISBN 9783540942580
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 Goedells 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. Fraisse's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic.
by "Nielsen BookData"