Axiomatizing Provable n-Provability
- Autores: Kolmakov E.A.1, Beklemishev L.D.1
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Afiliações:
- Steklov Mathematical Institute
- Edição: Volume 98, Nº 3 (2018)
- Páginas: 582-585
- Seção: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225587
- DOI: https://doi.org/10.1134/S1064562418070153
- ID: 225587
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Resumo
The set of all formulas whose n-provability in a given arithmetical theory S is provable in another arithmetical theory T is a recursively enumerable extension of S. We prove that such extensions can be naturally axiomatized in terms of transfinite progressions of iterated local reflection schemata over S. Specifically, the set of all provably 1-provable sentences in Peano arithmetic PA can be axiomatized by an ε0-times iterated local reflection schema over PA. The resulting characterizations provide additional information on the proof-theoretic strength of these theories and on the complexity of their axiomatization.
Sobre autores
E. Kolmakov
Steklov Mathematical Institute
Autor responsável pela correspondência
Email: kolmakov-ea@yandex.ru
Rússia, Moscow, 119991
L. Beklemishev
Steklov Mathematical Institute
Email: kolmakov-ea@yandex.ru
Rússia, Moscow, 119991
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