Handbook of Logic and Proof Techniques for Computer Science

1. Front Matter

   Pages i-xix

   PDF

2. Notation and First-Order Logic

   • Steven G. Krantz

   Pages 1-18

3. Semantics and Syntax

   • Steven G. Krantz

   Pages 19-24

4. Axiomatics and Formalism in Mathematics

   • Steven G. Krantz

   Pages 25-38

5. The Axioms of Set Theory

   • Steven G. Krantz

   Pages 39-42

6. Elementary Set Theory

   • Steven G. Krantz

   Pages 43-83

7. Recursive Functions

   • Steven G. Krantz

   Pages 85-94

8. The Number Systems

   • Steven G. Krantz

   Pages 95-106

9. Methods of Mathematical Proof

   • Steven G. Krantz

   Pages 107-120

10. The Axiom of Choice

    • Steven G. Krantz

    Pages 121-126

11. Proof Theory

    • Steven G. Krantz

    Pages 127-132

12. Category Theory

    • Steven G. Krantz

    Pages 133-143

13. Complexity Theory

    • Steven G. Krantz

    Pages 145-165

14. Boolean Algebra

    • Steven G. Krantz

    Pages 167-173

15. The Word Problem

    • Steven G. Krantz

    Pages 175-182

16. Back Matter

    Pages 183-245

    PDF

Logic is, and should be, the core subject area of modern mathemat­ ics. The blueprint for twentieth century mathematical thought, thanks to Hilbert and Bourbaki, is the axiomatic development of the subject. As a result, logic plays a central conceptual role. At the same time, mathematical logic has grown into one of the most recondite areas of mathematics. Most of modern logic is inaccessible to all but the special­ ist. Yet there is a need for many mathematical scientists-not just those engaged in mathematical research-to become conversant with the key ideas of logic. The Handbook of Mathematical Logic, edited by Jon Bar­ wise, is in point of fact a handbook written by logicians for other mathe­ maticians. It was, at the time of its writing, encyclopedic, authoritative, and up-to-the-moment. But it was, and remains, a comprehensive and authoritative book for the cognoscenti. The encyclopedic Handbook of Logic in Computer Science by Abramsky, Gabbay, and Maibaum is a wonderful resource for the professional. But it is overwhelming for the casual user. There is need for a book that introduces important logic terminology and concepts to the working mathematical scientist who has only a passing acquaintance with logic. Thus the present work has a different target audience. The intent of this handbook is to present the elements of modern logic, including many current topics, to the reader having only basic mathe­ matical literacy.

• Boolean algebra
• algorithms
• complexity
• complexity theory
• computability theory
• logic
• mathematical logic
• model theory
• proof theory
• set theory

"This is really what it promises to be—a good handbook: supple, self-contained, providing the necessary and sufficient working resources . . . it is more than [one] expect[s]: the rigor of usefulness and conciseness exceeds or equals . . . the pleasure of reading it."

—Zentralblatt Math

• Department of Mathematics, Washington University, St. Louis, USA

  Steven G. Krantz

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