Mathematical Logic, 3rd ed. 2021 Edition

Mathematical Logic, 3rd ed. 2021 Edition
PDF
  • eBook:
    Mathematical Logic, 3rd ed. 2021 Edition
  • Author:
    Heinz-Dieter Ebbinghaus, Jörg Flum, Wolfgang Thomas
  • Edition:
    3 edition
  • Categories:
  • Data:
    May 29, 2021
  • ISBN:
    3030738388
  • ISBN-13:
    9783030738389
  • Language:
    English
  • Pages:
    313 pages
  • Format:
    PDF

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

Content

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 Löwenheim–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. Computability and Its Limitations
11. Free Models and Logic Programming
12. An Algebraic Characterization of Elementary Equivalence
13. Lindström’s Theorems

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