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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
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.
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
Linking options:
https://www.mathnet.ru/eng/danma19 https://www.mathnet.ru/eng/danma/v499/p26
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Abstract page: | 101 | Full-text PDF : | 20 | References: | 22 |
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