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Arithmetic, proof theory, and computational complexity

Author: Peter Clote; Jan Krajíček
Publisher: Oxford [England] : Clarendon Press ; New York : Oxford University Press, ©1993.
Series: Oxford logic guides, 23.; Oxford science publications.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:

This book principally concerns the area of "Logical Complexity Theory", the study of bounded arithmetic, propositional proof systems, length of proof, etc and relations to computational complexity  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Peter Clote; Jan Krajíček
ISBN: 0198536909 9780198536901 0820519650 9780820519654
OCLC Number: 27070235
Description: xii, 428 pages : illustrations ; 25 cm.
Contents: Note on the existence of most general semi-unifiers / Matthias Baaz --
Kreisel's conjecture for L[backwards E]₁ (including a postscript by Georg Kreisel) / Matthias Baaz and Pavel Pudlák --
Number of symbols in Frege proofs with and without the deduction rule / Maria Luisa Bonet --
Algorithm for Boolean formula evaluation and for tree contraction / Samuel R. Buss --
Provably total functions in bounded arithmetic theories R₃, U₂ and V₂ / Samuel R. Buss, Jan Krajíc̆ek and Gaisi Takeuti --
On polynomial size Frege proofs of certain combinatorial principles / Peter Clote --
Interpretability and fragments of arithmetic / Petr Hájek --
Abbreviating proofs using metamathematical rules / Petr Hájek, Franco Montagna and Pavel Pudlák --
Open induction, Tennenbaum phenomena, and complexity theory / Richard Kaye --
Using Herbrand-type theorems to separate strong fragments of arithmetic / Richard Kaye --
An equivalence between second order bounded domain bounded arithmetic and first order bounded arithmetic / Alexander A. Razborov --
Integer parts of real closed exponential fields (extended abstract) / Jean-Pierre Ressayre --
Making infinite structures finite in models of second order bounded arithmetic / Søren Riis --
Ordinal arithmetic in I[triangle]₀ / Richard Sommer --
RSUV isomorphism / Gaisi Takeuti --
Feasible interpretability / Rineke Verbrugge.
Series Title: Oxford logic guides, 23.; Oxford science publications.
Responsibility: edited by Peter Clote and Jan Krajíček.
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This book is a valuable survey of the present state of research in this fascinating domain of foundational studies. It can certainly serve as an information and reference source as well as a source Read more...

 
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