Abstract
AbstractWe 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 depthdof the formulas in the original proof. Our results remove the constant of proportionality, giving an exponential stack of height equal tod−O(1). The proof method is based on more efficiently expressing the Gentzen–Solovay cut formulas as low depth formulas.
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