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• W3082725402 abstract "Beklemishev introduced an ordinal notation system for the Feferman-Schutte ordinal $Gamma_0$ based on the autonomous expansion of provability algebras. In this paper we present the logic $textbf{BC}$ (for Bracket Calculus). The language of $textbf{BC}$ extends said ordinal notation system to a strictly positive modal language. Thus, unlike other provability logics, $textbf{BC}$ is based on a self-contained signature that gives rise to an ordinal notation system instead of modalities indexed by some ordinal given a priori. The presented logic is proven to be equivalent to $textbf{RC}_{Gamma_0}$, that is, to the strictly positive fragment of $textbf{GLP}_{Gamma_0}$. We then define a combinatorial statement based on $textbf{BC}$ and show it to be independent of the theory $textbf{ATR}_0$ of Arithmetical Transfinite Recursion, a theory of second order arithmetic far more powerful than Peano Arithmetic." @default.
• W3082725402 created "2020-09-08" @default.
• W3082725402 creator A5051963513 @default.
• W3082725402 creator A5080309379 @default.
• W3082725402 date "2020-08-31" @default.
• W3082725402 modified "2023-09-27" @default.
• W3082725402 title "Deducibility and Independence in Beklemishev's Autonomous Provability Calculus" @default.
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