Handbook of Logic and Proof Techniques for Computer Science
Krantz, Steven G.
2002, XIX, 245 p.
A product of Birkhäuser Basel
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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.
Content Level »Professional/practitioner
Keywords »Boolean algebra - algorithms - complexity - complexity theory - computability theory - logic - mathematical logic - model theory - proof theory - set theory
Preface Notation and First-Order Logic Semantics and Syntax Axiomatics and Formalism in Mathematics The Axioms of Set Theory Elementary Set Theory Recursive Functions The Number Systems Methods of Mathematical Proof The Axiom of Choice Proof Theory Category Theory Complexity Theory Boolean Algebra The Word Problem List of Notation and Logic Glossary Terms from Mathematical and Sentential Logic A Guide to the Literature Bibliography Index