Mathematical Logic Quarterly 54 (6):629-640 (2008)

Abstract
In this paper we show some non-elementary speed-ups in logic calculi: Both a predicative second-order logic and a logic for fixed points of positive formulas are shown to have non-elementary speed-ups over first-order logic. Also it is shown that eliminating second-order cut formulas in second-order logic has to increase sizes of proofs super-exponentially, and the same in eliminating second-order epsilon axioms. These are proved by relying on results due to P. Pudlák
Keywords epsilon calculi  second‐order logic  Speed‐up
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DOI 10.1002/malq.200710067
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References found in this work BETA

Elimination Theorems of Uniqueness Conditions.Nobuyoshi Motohashi - 1982 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 28 (33-38):511-524.
Elimination Theorems of Uniqueness Conditions.Nobuyoshi Motohashi - 1982 - Mathematical Logic Quarterly 28 (33‐38):511-524.

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Intuitionistic Fixed Point Theories Over Set Theories.Toshiyasu Arai - 2015 - Archive for Mathematical Logic 54 (5-6):531-553.

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