Axiomatizing Provable n-Provability


Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Somente assinantes

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

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML

Declaração de direitos autorais © Pleiades Publishing, Ltd., 2018