Mathematical Logic

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.

List 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

Report

"...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

Product details

• Authors: H- Ebbinghaus, H - Ebbinghaus, H. -D Ebbinghaus, H. -D. Ebbinghaus, H.-D. Ebbinghaus, Flum, J. Flum, Wolfgang Thomas
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 22.04.2014
• EAN: 9781475723571
• ISBN: 978-1-4757-2357-1
• No. of pages: 291
• Dimensions: 146 mm x 18 mm x 236 mm
• Weight: 468 g
• Series: Undergraduate Texts in Mathematics; Undergraduate Texts in Mathematics; Undergraduate Texts in Mathema
• Subjects: Humanities, art, music > Education; Natural sciences, medicine, IT, technology > Mathematics > Basic principles