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On Herbrand consistency in weak arithmetic

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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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Received: 22 September 1997 / Revised version: 27 March 2000 /¶Published online: 15 June 2001

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Adamowicz, Z., Zbierski, P. On Herbrand consistency in weak arithmetic. Arch. Math. Logic 40, 399–413 (2001). https://doi.org/10.1007/s001530000072

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  • DOI: https://doi.org/10.1007/s001530000072

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