Journal
STUDIA LOGICA
Volume 106, Issue 2, Pages 219-235Publisher
SPRINGER
DOI: 10.1007/s11225-017-9735-y
Keywords
Provability logic; Arithmetical completeness theorem; Formalized arithmetic; Numerations
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Funding
- JSPS KAKENHI [16K17653]
- Grants-in-Aid for Scientific Research [17H02263, 16K17653] Funding Source: KAKEN
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We prove that for any recursively axiomatized consistent extension T of Peano Arithmetic, there exists a provability predicate of T whose provability logic is precisely the modal logic . For this purpose, we introduce a new bimodal logic , and prove the Kripke completeness theorem and the uniform arithmetical completeness theorem for .
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