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

• Autorzy: Zofia Adamowicz , Konrad Zdanowski
• Języki publikacji: EN

Abstrakty

EN

We prove that for i ≥ 1, the arithmetic $IΔ₀ + Ω_i$ does not prove a variant of its own Herbrand consistency restricted to the terms of depth in $(1+ε)log^{i+2}$, 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 $log^{i+3}$.

Kategorie tematyczne

• 03F40: G\"odel numberings and issues of incompleteness
• 03F30: First-order arithmetic and fragments

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2011
• Tom: 212
• Numer: 3
• Strony: 191-216

Daty

wydano

2011

Twórcy

autor

Zofia Adamowicz

• Institute of Mathematics, Polish Academy of Sciences, 00-956 Warszawa, Poland

autor

Konrad Zdanowski

• Institute of Mathematics, Polish Academy of Sciences, 00-956 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm212-3-1