Notes on polynomially bounded arithmetic

Journal of Symbolic Logic 61 (3):942-966 (1996)
We characterize the collapse of Buss' bounded arithmetic in terms of the provable collapse of the polynomial time hierarchy. We include also some general model-theoretical investigations on fragments of bounded arithmetic
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DOI 10.2307/2275794
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References found in this work BETA
Bounded Arithmetic and the Polynomial Hierarchy.Jan Krajíček, Pavel Pudlák & Gaisi Takeuti - 1991 - Annals of Pure and Applied Logic 52 (1-2):143-153.
∑11-Formulae on Finite Structures.M. Ajtai - 1983 - Annals of Pure and Applied Logic 24 (1):1-48.
Exponentiation and Second-Order Bounded Arithmetic.Jan Krajíček - 1990 - Annals of Pure and Applied Logic 48 (3):261-276.

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Citations of this work BETA
Relating the Bounded Arithmetic and Polynomial Time Hierarchies.Samuel R. Buss - 1995 - Annals of Pure and Applied Logic 75 (1-2):67-77.
The Strength of Extensionality II—Weak Weak Set Theories Without Infinity.Kentaro Sato - 2011 - Annals of Pure and Applied Logic 162 (8):579-646.
On Theories of Bounded Arithmetic For.Emil Jeřábek - 2011 - Annals of Pure and Applied Logic 162 (4):322-340.
Short Propositional Refutations for Dense Random 3CNF Formulas.Sebastian Müller & Iddo Tzameret - 2014 - Annals of Pure and Applied Logic 165 (12):1864-1918.

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