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• W1994332324 abstract "We suggest an algebraic approach to proof-theoretic analysis based on the notion of graded provability algebra, that is, Lindenbaum boolean algebra of a theory enriched by additional operators which allow for the structure to capture proof-theoretic (syntax-sensitive) information. We use this method to analyze Peano arithmetic and show how an ordinal notation system up to ε0 can be recovered from the corresponding algebra in a canonical way. This method also establishes links between proof-theoretic ordinal analysis and the work which has been done in the last two decades on provability logic and reflection principles. Because of its abstract algebraic nature, we hope that it will also be of interest for non-prooftheorists." @default.
• W1994332324 created "2016-06-24" @default.
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• W1994332324 date "2004-08-01" @default.
• W1994332324 modified "2023-09-25" @default.
• W1994332324 title "Provability algebras and proof-theoretic ordinals, I" @default.
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• W1994332324 doi "https://doi.org/10.1016/j.apal.2003.11.030" @default.
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