On the completeness principle: A study of provability in Heyting's Arithmetic and extensions

Annals of Mathematical Logic 22 (3):263 (1982)
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10.1016/0003-4843(82)90024-9

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Provability logic and the completeness principle.Albert Visser & Jetze Zoethout - 2019 - Annals of Pure and Applied Logic 170 (6):718-753.
Rules and Arithmetics.Albert Visser - 1999 - Notre Dame Journal of Formal Logic 40 (1):116-140.
The Σ1-provability logic of HA.Mohammad Ardeshir & Mojtaba Mojtahedi - 2018 - Annals of Pure and Applied Logic 169 (10):997-1043.
Intermediate Logics and the de Jongh property.Dick de Jongh, Rineke Verbrugge & Albert Visser - 2011 - Archive for Mathematical Logic 50 (1-2):197-213.

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