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

Zofia Adamowicz; Konrad Zdanowski

Fundamenta Mathematicae, Tome 215 (2011), p. 191-216 / Harvested from The Polish Digital Mathematics Library

Résumé

We prove that for i ≥ 1, the arithmetic $I Δ ₀ + Ω_{i}$ does not prove a variant of its own Herbrand consistency restricted to the terms of depth in $(1 + ε) l o g^{i + 2}$ , where ε is an arbitrarily small constant greater than zero. On the other hand, the provability holds for the set of terms of depths in $l o g^{i + 3}$ .

Publié le : 2011-01-01

Zbl 1256.03062

EUDML-ID : urn:eudml:doc:283125

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     author = {Zofia Adamowicz and Konrad Zdanowski},
     title = {Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics},
     journal = {Fundamenta Mathematicae},
     volume = {215},
     year = {2011},
     pages = {191-216},
     zbl = {1256.03062},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-3-1}
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Zofia Adamowicz; Konrad Zdanowski. Lower and upper bounds for the provability of Herbrand consistency in weak arithmetics. Fundamenta Mathematicae, Tome 215 (2011) pp. 191-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm212-3-1/