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Diagonalizable algebras and the length of proofs

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Title: Diagonalizable algebras and the length of proofs
Authors: Adamsson, Gunnar
Issue Date: 28-Nov-2011
Degree: Student essay
Abstract: We rederive a theorem of Shavrukov [17] on the diagonaliz- able algebras of PA and ZF using an approach that differs ever-so slightly from the original. This gives a somewhat stronger result (which was im- plicit in the original proof) that we, coupled with a more careful analysis of the Parikh speed-up phenomenon, put to use by giving examples of how different choices of provability predicates for a given theory T can lead to non-isomorphic algebras. We also show that, by a minor tweak, t... more
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