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Several of the most well-known results on provability algebras of arithmetical theories were obtained by V. Yu. Shavrukov. In particular, he provided sufficient conditions for the existence and non-existence of isomorphisms between such algebras. Later the improvements to Shavrukov's non-isomorphism theorem were found by G. Adamsson. We discuss further refinements of these results and possible applications to the case of bimodal provability algebras.