Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics
Zofia Adamowicz, Konrad Zdanowski · Fundamenta Mathematicae · 2011
We prove that for $i\geq 1$, the arithmetic ${\rm I}\Delta_0 + \Omega_i$ does not prove a variant of its own Herbrand consistency restricted to the terms of depth in $(1+\varepsilon)\log^{i+2}$, where $\varepsilon$ is an arbitrarily small constant great