Herbrand consistency and bounded arithmetic

Zofia Adamowicz. "Herbrand consistency and bounded arithmetic." Fundamenta Mathematicae 171.3 (2002): 279-292. <http://eudml.org/doc/282735>.

@article{ZofiaAdamowicz2002,
abstract = {We prove that the Gödel incompleteness theorem holds for a weak arithmetic Tₘ = IΔ₀ + Ωₘ, for m ≥ 2, in the form Tₘ ⊬ HCons(Tₘ), where HCons(Tₘ) is an arithmetic formula expressing the consistency of Tₘ with respect to the Herbrand notion of provability. Moreover, we prove $Tₘ ⊬ HCons^\{Iₘ\}(Tₘ)$, where $HCons^\{Iₘ\}$ is HCons relativised to the definable cut Iₘ of (m-2)-times iterated logarithms. The proof is model-theoretic. We also prove a certain non-conservation result for Tₘ.},
author = {Zofia Adamowicz},
journal = {Fundamenta Mathematicae},
keywords = {Gödel’s incompleteness theorem; weak arithmetic; provability; Herbrand consistency; bounded arithmetic},
language = {eng},
number = {3},
pages = {279-292},
title = {Herbrand consistency and bounded arithmetic},
url = {http://eudml.org/doc/282735},
volume = {171},
year = {2002},
}

TY - JOUR
AU - Zofia Adamowicz
TI - Herbrand consistency and bounded arithmetic
JO - Fundamenta Mathematicae
PY - 2002
VL - 171
IS - 3
SP - 279
EP - 292
AB - We prove that the Gödel incompleteness theorem holds for a weak arithmetic Tₘ = IΔ₀ + Ωₘ, for m ≥ 2, in the form Tₘ ⊬ HCons(Tₘ), where HCons(Tₘ) is an arithmetic formula expressing the consistency of Tₘ with respect to the Herbrand notion of provability. Moreover, we prove $Tₘ ⊬ HCons^{Iₘ}(Tₘ)$, where $HCons^{Iₘ}$ is HCons relativised to the definable cut Iₘ of (m-2)-times iterated logarithms. The proof is model-theoretic. We also prove a certain non-conservation result for Tₘ.
LA - eng
KW - Gödel’s incompleteness theorem; weak arithmetic; provability; Herbrand consistency; bounded arithmetic
UR - http://eudml.org/doc/282735
ER -