Samuel R. Buss.
"Sharpened Lower Bounds for Cut Elimination."
Journal of Symbolic Logic 77, 2 (2012) 656-668.
Download manuscript: PDF.
Abstract: We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our results remove the constant of proportionality, giving an exponential stack of height equal to d-O(1). The proof method is based on more efficiently expressing the Gentzen-Solovay cut formulas as low depth formulas.
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