Herbrand Consistency of Some Finite Fragments of Bounded Arithmetical Theories

Details Herbrand Consistency of Some Finite Fragments of Bounded Arithmetical Theories Herbrand Consistency of Some Finite Fragments of Bounded Arithmetical Theories

2011-10-09

arxiv.org/abs/1110.1848v1

Mathematics

Logic

14 pages

Scientific paper

We formalize the notion of Herbrand Consistency in an appropriate way for bounded arithmetics, and show the existence of a finite fragment of ${\rm I\Delta_0}$ whose Herbrand Consistency is not provable in the thoery ${\rm I\Delta_0}$. We also show the existence of an ${\rm I\Delta_0}-$derivable $\Pi_1-$sentence such that ${\rm I\Delta_0}$ cannot prove its Herbrand Consistency.

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