
Mathematical Logic
Springer (Publisher)
2nd Edition
Published on 10. June 1994
Book
Hardback
X, 291 pages
978-0-387-94258-2 (ISBN)
Description
What is a mathematical proof? How can proofs be justified? Are there limitations to provability? To what extent can machines carry out mathe matical proofs? Only in this century has there been success in obtaining substantial and satisfactory answers. The present book contains a systematic discussion of these results. The investigations are centered around first-order logic. Our first goal is Godel's completeness theorem, which shows that the con sequence relation coincides with formal provability: By means of a calcu lus consisting of simple formal inference rules, one can obtain all conse quences of a given axiom system (and in particular, imitate all mathemat ical proofs). A short digression into model theory will help us to analyze the expres sive power of the first-order language, and it will turn out that there are certain deficiencies. For example, the first-order language does not allow the formulation of an adequate axiom system for arithmetic or analysis. On the other hand, this difficulty can be overcome--even in the framework of first-order logic-by developing mathematics in set-theoretic terms. We explain the prerequisites from set theory necessary for this purpose and then treat the subtle relation between logic and set theory in a thorough manner.
Reviews / Votes
".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
More details
Series
Edition
Second Edition 1994
Language
English
Place of publication
New York
United States
Target group
Lower undergraduate
Edition type
New edition
Illustrations
X, 291 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 22 mm
Weight
629 gr
ISBN-13
978-0-387-94258-2 (9780387942582)
DOI
10.1007/978-1-4757-2355-7
Schweitzer Classification
Other editions
Additional editions

H.-D. Ebbinghaus | J. Flum | Wolfgang Thomas
Mathematical Logic
Book
12/2012
2nd Edition
Springer
€64.15
Article exhausted; check for reprint
Persons
Content
A.- 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 Limitations of the Formal Method.- XI Free Models and Logic Programming.- XII An Algebraic Characterization of Elementary Equivalence.- XIII Lindström's Theorems.- References.- Symbol Index.