Axiomatizing Provable n-Provability View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-11

AUTHORS

E. A. Kolmakov, L. D. Beklemishev

ABSTRACT

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. More... »

PAGES

582-585

References to SciGraph publications

Journal

TITLE

Doklady Mathematics

ISSUE

3

VOLUME

98

Author Affiliations

Identifiers

URI

http://scigraph.springernature.com/pub.10.1134/s1064562418070153

DOI

http://dx.doi.org/10.1134/s1064562418070153

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1111224412


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