Arithmetic, proof theory, and computational complexity

CLOTE Peter & KRAJICEK Jan (Eds)

ISBN 10: 0198536909 / ISBN 13: 9780198536901

Published by Oxford: Clarendon Press, 1993

About this Item

pp.xii,428, hardback (publisher's dark blue cloth, a broad gilt-lettered red band taking up most of the spine, at the bottom of which is the OUP open-book logo in gilt), a near-fine ex-library copy (no dust-jacket) of a book in the Oxford Logic Guides series [0198536909].

Seller Inventory # 160018

Bibliographic Details

• Title: Arithmetic, proof theory, and computational complexity
• Publisher: Oxford: Clarendon Press
• Publication Date: 1993
• Language: English
• ISBN 10: 0198536909
• ISBN 13: 9780198536901
• Binding: Hardcover
• Condition: Very Good
• Seller catalogs:
  • 654

About this title

Synopsis

This book principally concerns the rapidly growing area of what might be termed "Logical Complexity Theory": the study of bounded arithmetic, propositional proof systems, length of proof, and similar themes, and the relations of these topics to computational complexity theory. Issuing from a two-year international collaboration, the book contains articles concerning the existence of the most general unifier, a special case of Kreisel's conjecture on length-of-proof, propositional logic proof size, a new alternating logtime algorithm for boolean formula evaluation and relation to branching programs, interpretability between fragments of arithmetic, feasible interpretability, provability logic, open induction, Herbrand-type theorems, isomorphism between first and second order bounded arithmetics, forcing techniques in bounded arithmetic, and ordinal arithmetic in Λ Δ [o. Also included is an extended abstract of J.P. Ressayre's new approach concerning the model completeness of the theory of real closed exponential fields. Additional features of the book include the transcription and translation of a recently discovered 1956 letter from Kurt Godel to J. von Neumann, asking about a polynomial time algorithm for the proof in k-symbols of predicate calculus formulas (equivalent to the P-NP question); and an open problem list consisting of seven fundamental and 39 technical questions contributed by many researchers, together with a bibliography of relevant references. This scholarly work will interest mathematical logicians, proof and recursion theorists, and researchers in computational complexity.

About the Author

Peter Clote is at Boston College, . Jan Krajícek is at Ceskoslovenská Akademie Ved Praha 1.