Count(ifq) does not imply Count

Annals of Pure and Applied Logic 90 (1-3):1-56 (1997)
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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 q

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10.1016/s0168-0072(97)00029-8

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Søren Riis
Roskilde University

Citations of this work

The complexity of propositional proofs.Nathan Segerlind - 2007 - Bulletin of Symbolic Logic 13 (4):417-481.

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References found in this work

Bounded arithmetic, propositional logic, and complexity theory.Jan Krajíček - 1995 - New York, NY, USA: Cambridge University Press.
¹1-formulae on finite structures.M. Ajtai - 1983 - Annals of Pure and Applied Logic 24 (1):1.

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