Geodesic
Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics
Zofia Adamowicz1 ; Konrad Zdanowski1
1 Institute of Mathematics Polish Academy of Sciences 00-956 Warszawa, Poland
Fundamenta Mathematicae, Tome 212 (2011) no. 3, pp. 191-216

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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 $\log^{i+3}$.
DOI : 10.4064/fm212-3-1
Keywords: prove geq arithmetic delta omega does prove variant its own herbrand consistency restricted terms depth varepsilon log where varepsilon arbitrarily small constant greater zero other provability holds set terms depths log

Zofia Adamowicz 1 ; Konrad Zdanowski 1

1 Institute of Mathematics Polish Academy of Sciences 00-956 Warszawa, Poland 
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Zofia Adamowicz; Konrad Zdanowski. Lower and upper bounds for the provability of Herbrand consistency
in weak arithmetics. Fundamenta Mathematicae, Tome 212 (2011) no. 3, pp. 191-216. doi: 10.4064/fm212-3-1

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