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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2021, Volume 499, Pages 26–30
DOI: https://doi.org/10.31857/S2686954321040081 (Mi danma19) 		 
MATHEMATICS

On a strengthening of the non-isomorphism theorem for provability algebras

E. A. Kolmakovab

a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
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DOI: https://doi.org/10.31857/S2686954321040081
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 19-31-9005
The reported study was funded by the Russian Foundation for Basic Research, project no. 19-31-90050.
Presented: L. D. Beklemishev
Received: 29.04.2021
Revised: 29.04.2021
Accepted: 15.05.2021
English version:
Doklady Mathematics, 2021, Volume 104, Issue 1, Pages 180–183
DOI: https://doi.org/10.1134/S1064562421040086
Bibliographic databases:
Document Type: Article
UDC: 510.6
Language: Russian
Citation: E. A. Kolmakov, “On a strengthening of the non-isomorphism theorem for provability algebras”, Dokl. RAN. Math. Inf. Proc. Upr., 499 (2021), 26–30; Dokl. Math., 104:1 (2021), 180–183
Citation in format AMSBIB
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