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Count(ifq) does not imply Count
Annals of Pure and Applied Logic 90 (1-3):1-56 (1997)
Abstract
It is shown that the elementary principles Count and Count are logically independent in the system IΔ0 of Bounded Arithmetic. More specifically it is shown that Count implies Count exactly when each prime factor in p is a factor in qAuthor's Profile
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Citations of this work
The complexity of propositional proofs.Nathan Segerlind - 2007 - Bulletin of Symbolic Logic 13 (4):417-481.
References found in this work
The relative efficiency of propositional proof systems.Stephen A. Cook & Robert A. Reckhow - 1979 - Journal of Symbolic Logic 44 (1):36-50.
Bounded arithmetic, propositional logic, and complexity theory.Jan Krajíček - 1995 - New York, NY, USA: Cambridge University Press.
Polynomial size proofs of the propositional pigeonhole principle.Samuel R. Buss - 1987 - Journal of Symbolic Logic 52 (4):916-927.
Provability of the pigeonhole principle and the existence of infinitely many primes.J. B. Paris, A. J. Wilkie & A. R. Woods - 1988 - Journal of Symbolic Logic 53 (4):1235-1244.
Combinatorial principles in elementary number theory.Alessandro Berarducci & Benedetto Intrigila - 1991 - Annals of Pure and Applied Logic 55 (1):35-50.
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