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arXiv · 1110.1848

Herbrand Consistency of Some Finite Fragments of Bounded Arithmetical Theories

Saeed Salehi
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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 ${\rm I\Delta_0}$ 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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BibTeXRIS

Saeed Salehi. 2011-10-09. Herbrand Consistency of Some Finite Fragments of Bounded Arithmetical Theories. https://doi.org/10.1007/s00153-012-0318-3

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