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Paper   IPM / M / 12801
School of Mathematics
  Title:   Herbrand consistency of some finite fragments of bounded arithmetical theories
  Author(s):  S. Salehi
  Status:   Published
  Journal: Arch. Math. Logic
  Vol.:  52
  Year:  2013
  Pages:   317-333
  Supported by:  IPM
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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