Herbrand Consistency of Some Finite Fragments of Bounded Arithmetical Theories

Abstract

We formalize the notion of Herbrand Consistency in an appropriate way for bounded arithmetics, and show the existence of a finite fragment of $\mathrm{I}{\mathrm{\Delta }}_0$ whose Herbrand Consistency is not provable in the thoery $\mathrm{I}{\mathrm{\Delta }}_0$. We also show the existence of an $\mathrm{I}{\mathrm{\Delta }}_0-$derivable ${\Pi }_1-$sentence such that $\mathrm{I}{\mathrm{\Delta }}_0$ cannot prove its Herbrand Consistency.

References in corpus (2)

• Herbrand Consistency of Some Arithmetical Theories
• Separating Bounded Arithmetics by Herbrand Consistency

Cited by in corpus (1)

• Herbrand Consistency of Some Arithmetical Theories