Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics

Volume 212 / 2011

Zofia Adamowicz, Konrad Zdanowski Fundamenta Mathematicae 212 (2011), 191-216 MSC: Primary 03F30; Secondary 03F40. DOI: 10.4064/fm212-3-1

Abstract

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 greater than zero. On the other hand, the provability holds for the set of terms of depths in $\log^{i+3}$.

Authors

  • Zofia AdamowiczInstitute of Mathematics
    Polish Academy of Sciences
    00-956 Warszawa, Poland
    e-mail
  • Konrad ZdanowskiInstitute of Mathematics
    Polish Academy of Sciences
    00-956 Warszawa, Poland
    e-mail

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