Bounded arithmetic AID for Frege system
Logic
2016-09-07 v1
Abstract
In this paper we introduce a system AID (Alogtime Inductive Definitions) of bounded arithmetic. The main feature of AID is to allow a form of inductive definitions, which was extracted from Buss' propositional consistency proof of Frege systems F. We show that AID proves the soundness of F, and conversely any \Sigma^b_0-theorem in AID yields boolean sentences of which F has polysize proofs. Further we define \Sigma^b_1-faithful interpretations between AID + \Sigma b^_0 - CA and a quantified theory QALV of an equational system ALV in P. Clote. Hence ALV also proves the soundness of F.
Cite
@article{arxiv.math/9809205,
title = {Bounded arithmetic AID for Frege system},
author = {Toshiyasu Arai},
journal= {arXiv preprint arXiv:math/9809205},
year = {2016}
}