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Archive for Mathematical Logic

, Volume 52, Issue 3–4, pp 317–333 | Cite as

Herbrand consistency of some finite fragments of bounded arithmetical theories

  • Saeed Salehi
Article

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 Π 1-sentence such that IΔ0 cannot prove its Herbrand Consistency.

Keywords

Herbrand consistency Bounded arithmetic Gödel’s Second Incompleteness Theorem 

Mathematics Subject Classification (2000)

03F40 03F25 03F30 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TabrizTabrizIran
  2. 2.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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