The provably total NP search problems of weak second order bounded arithmetic

Annals of Pure and Applied Logic 162 (6):419-446 (2011)
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Abstract

We define a new NP search problem, the “local improvement” principle, about labellings of an acyclic, bounded-degree graph. We show that, provably in , it characterizes the consequences of and that natural restrictions of it characterize the consequences of and of the bounded arithmetic hierarchy. We also show that over V0 it characterizes the consequences of V1 and hence that, in some sense, a miniaturized version of the principle gives a new characterization of the consequences of . Throughout our search problems are “type-2” NP search problems, which take second-order objects as parameters

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Phuong Nguyen
University of Georgia

Citations of this work

Incompleteness in the Finite Domain.Pavel Pudlák - 2017 - Bulletin of Symbolic Logic 23 (4):405-441.
The canonical pairs of bounded depth Frege systems.Pavel Pudlák - 2021 - Annals of Pure and Applied Logic 172 (2):102892.

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