Geodesic
On a strengthening of the non-isomorphism theorem for provability algebras
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 26-30

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We prove a strengthened version of V. Shavrukov’s result on the non-isomorphism of provability algebras of two $\Sigma_1$-sound theories, based on the improvements previously discovered by G. Adamsson. We then obtain several corollaries to the strengthened result by applying it to various pairs of theories and obtain new non-isomorphism examples. In particular, we show that there are no epimorphisms from $(\mathfrak{L}_T,\square_T\square_T)$ onto $(\mathfrak{L}_T,\square_T)$.
Keywords: provability predicate, provability algebra, reflection principle. 
@article{DANMA_2021_499_a5,
     author = {E. A. Kolmakov},
     title = {On a strengthening of the non-isomorphism theorem for provability algebras},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {26--30},
     publisher = {mathdoc},
     volume = {499},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2021_499_a5/}
}
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E. A. Kolmakov. On a strengthening of the non-isomorphism theorem for provability algebras. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 499 (2021), pp. 26-30. http://geodesic.mathdoc.fr/item/DANMA_2021_499_a5/