Archive for Mathematical Logic 40 (6):399-413 (2001)

Abstract
We prove that the Gödel incompleteness theorem holds for a weak arithmetic T = IΔ0 + Ω2 in the form where Cons H (T) is an arithmetic formula expressing the consistency of T with respect to the Herbrand notion of provability
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DOI 10.1007/s001530000072
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Passive Induction and a Solution to a Paris–Wilkie Open Question.Dan E. Willard - 2007 - Annals of Pure and Applied Logic 146 (2):124-149.
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