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Mathematical Logic : Undergraduate Texts in Mathematics - H-. D. Ebbinghaus

Mathematical Logic

Undergraduate Texts in Mathematics


Published: 15th November 1996
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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. Fraisse's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic.

"...the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level." - Journal of Symbolic Logic

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
Lindstroem's Theorems
Symbol Index
Subject Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387942582
ISBN-10: 0387942580
Series: Undergraduate Texts in Mathematics
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 291
Published: 15th November 1996
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.7 x 16.9  x 2.1
Weight (kg): 0.61
Edition Number: 2
Edition Type: Revised