Geodesic
The Lengths of Proofs: Kreisel's conjecture and G\"odel's speed-up theorem
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XI, Tome 358 (2008), pp. 153-188

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We collect and compare several results which have been obtained so far in the attempts to prove a statement conjectured by Kreisel, about the lengths of proofs. We also survey several results regarding a speed-up theorem announced by Gödel in an abstract published in 1936. Finally we connect this to Kreisel's conjecture. Bibl. – 63 titles. 
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     title = {The {Lengths} of {Proofs:} {Kreisel's} conjecture and {G\"odel's} speed-up theorem},
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S. Cavagnetto. The Lengths of Proofs: Kreisel's conjecture and G\"odel's speed-up theorem. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part XI, Tome 358 (2008), pp. 153-188. http://geodesic.mathdoc.fr/item/ZNSL_2008_358_a8/