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Mathematical Logic

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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 Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

Author(s): H.-D. Ebbinghaus, J. Flum, W. Thomas
Series: Undergraduate Texts in Mathematics
Edition: 2nd
Publisher: Springer
Year: 1994

Language: English
Pages: 289

Front Matter....Pages i-x
Front Matter....Pages 1-1
Introduction....Pages 3-9
Syntax of First-Order Languages....Pages 11-25
Semantics of First-Order Languages....Pages 27-57
A Sequent Calculus....Pages 59-74
The Completeness Theorem....Pages 75-85
The Löwenheim-Skolem Theorem and the Compactness Theorem....Pages 87-98
The Scope of First-Order Logic....Pages 99-114
Syntactic Interpretations and Normal Forms....Pages 115-133
Front Matter....Pages 135-135
Extensions of First-Order Logic....Pages 137-149
Limitations of the Formal Method....Pages 151-187
Free Models and Logic Programming....Pages 189-241
An Algebraic Characterization of Elementary Equivalence....Pages 243-259
Lindström’s Theorems....Pages 261-276
Back Matter....Pages 277-290