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- W2949202275 abstract "Beklemishev introduced an ordinal notation system for the Feferman-Schutte ordinal (varGamma _0) based on the autonomous expansion of provability algebras. In this paper we present the logic (mathbf {BC}) (for Bracket Calculus). The language of (mathbf {BC}) extends said ordinal notation system to a strictly positive modal language. Thus, unlike other provability logics, (mathbf {BC}) is based on a purely modal signature that gives rise to an ordinal notation system instead of modalities indexed by some ordinal given a priori. Moreover, since the order between these notations can be established in terms of derivability within the calculus, the inferences in this system can be carried out without using any external property of ordinals. The presented logic is proven to be equivalent to (varvec{mathbf {RC}_{varGamma _0}}), that is, to the strictly positive fragment of (varvec{mathbf {GLP}_{varGamma _0}})." @default.
- W2949202275 created "2019-06-27" @default.
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- W2949202275 date "2019-01-01" @default.
- W2949202275 modified "2023-09-25" @default.
- W2949202275 title "A Self-contained Provability Calculus for $$varGamma _0$$" @default.
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- W2949202275 doi "https://doi.org/10.1007/978-3-662-59533-6_12" @default.
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