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math.LO2021
On Shavrukov's non-isomorphism theorem for diagonalizable algebras
Evgeny A. Kolmakov
We prove a strengthened version of V. Yu. Shavrukov's result on the non-isomorphism of diagonalizable algebras of two -sound theories, based on the improvements previously fou…
math.LO2019
Local reflection, definable elements and 1-provability
Evgeny Kolmakov
In this note we study several topics related to the schema of local reflection and its partial and relativized variants. Firstly, we introduce the principle of un…
math.LO2018
Axiomatizing provable -provability
Evgeny Kolmakov, Lev Beklemishev
A formula is called \emph{-provable} in a formal arithmetical theory if is provable in together with all true arithmetical -sentences taken as additional…