Bounded arithmetic in free logic
type: Item
instance of: scholarly article
zbMATH Open document ID: 1252.03137
DOI: 10.2168/LMCS-8(3:7)2012
author: Yoriyuki Yamagata
published in: Logical Methods in Computer Science
publication date: 2012-08-15T00:00:00Z
full work available at URL: https://arxiv.org/abs/1201.3733
Mathematics Subject Classification ID: 03F30
zbMATH DE Number: 6066149
zbMATH Keywords: bounded arithmetic
zbMATH Keywords: free logic
zbMATH Keywords: finitistic Gödel sentences
MaRDI profile type: Publication
arXiv ID: 1201.3733
title: Bounded arithmetic in free logic
review text: The paper is devoted to the open problem whether Buss's hierarchy of theories of bounded arithmetic collapses or not. Buss's theories are reformulated using free logic. It is conjectured that such theories are easier to handle. To show this, it is proved that Buss's theories prove consistencies of induction-free fragments of introduced theories whose formulae have bounded complexity. It is also shown that theories in Buss's hierarchy can be interpreted in the introduced theories using a simple translation. Finally, finitistic Gödel sentences in the developed systems are investigated. The aim here is the hope of proving that a theory in a lower level of Buss's hierarchy cannot prove consistency of induction-free fragments of introduced theories whose formulae have higher complexity.
reviewed by: Roman Murawski
description: scientific article; zbMATH DE number 6066149