Herbrand consistency of some finite fragments of bounded arithmetical theories

Archive for Mathematical Logic 52 (3-4):317-333 (2013)
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Abstract

We formalize the notion of Herbrand Consistency in an appropriate way for bounded arithmetics, and show the existence of a finite fragment of IΔ0 whose Herbrand Consistency is not provable in IΔ0. We also show the existence of an IΔ0-derivable Π1-sentence such that IΔ0 cannot prove its Herbrand Consistency.

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10.1007/s00153-012-0318-3

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Saeed Salehi
University of Tabriz

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On Herbrand consistency in weak arithmetic.Zofia Adamowicz & Paweł Zbierski - 2001 - Archive for Mathematical Logic 40 (6):399-413.
Passive induction and a solution to a Paris–Wilkie open question.Dan E. Willard - 2007 - Annals of Pure and Applied Logic 146 (2-3):124-149.
Herbrand consistency of some arithmetical theories.Saeed Salehi - 2012 - Journal of Symbolic Logic 77 (3):807-827.

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