Handbook of Logic and Proof Techniques for Computer Science - Hardcover

Krantz, Steven G.

Hardcover

ISBN 10: 081764220X ISBN 13: 9780817642204

Publisher: Birkhäuser, 2002

Synopsis

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.

About this title

Review

"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

Synopsis

This handbook presents the elements of modern logic, including many current topics, to the reader having only basic mathematical literacy. Computer scientists will find specific examples and important ideas such as axiomatics, recursion theory, decidability, independence, completeness, consistency, model theory, and P/NP completeness. The book contains definitions, examples and discussion of all of the key ideas in basic logic, but also makes a special effort to cut through the mathematical formalism, difficult notation, and esoteric terminology that is typical of modern mathematical logic. The Handbook of Mathematical Logic and Proof Techniques delivers cogent and self-contained introductions to critical advanced topics, including: - Godel's completeness and incompleteness theorems - Methods of proof, cardinal and ordinal numbers, the continuum hypothesis, the axiom of choice, model theory, number systems and their construction - Extensive treatment of complexity theory and programming applications - Presents applications to algorithms in Boolean algebra - Provides a treatment of set theory and applications of logic

Edition details

• Publisher: Birkhäuser
• Publication date: 2002
• ISBN 10: 081764220X
• ISBN 13: 9780817642204
• Binding: Hardcover
• Language: English
• Number of pages: 264