Diagonalizable algebras and the length of proofs
Sammanfattning
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, the in-
jectivity assumption can be dropped and the result extended to arbitrary
epimorphisms.
Examinationsnivå
Student essay