The elementary theory of the natural lattice is finitely axiomatizable
type: Item
instance of: scholarly article
title: The elementary theory of the natural lattice is finitely axiomatizable
zbMATH Open document ID: 0704.03012
published in: Notre Dame Journal of Formal Logic
publication date: 1989-01-01T00:00:00Z
review text: The author investigates the first order theory of the structure (\({\mathcal N}^*,|)\), where \({\mathcal N}^*\) is the set of positive integers and \(|\) is the divisibility relation. It is known that this theory, called DIV is consistent, complete, decidable and not categorical. In this paper it is shown that DIV is finitely axiomatizable. The author gives an explicit finite axiomatization of DIV and verifies the completeness of it by the method of elimination of quantifiers. In the proof some unpublished results obtained by the author in 1979 are used.
Mathematics Subject Classification ID: 03C07
Mathematics Subject Classification ID: 03C10
zbMATH DE Number: 4154414
zbMATH Keywords: positive integers with divisibility
zbMATH Keywords: divisibility relation
zbMATH Keywords: finite axiomatization of DIV
author: Patrick Cégielski
reviewed by: Agnieszka Wojciechowska-Waszkiewicz
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093635001
OpenAlex ID: W2078092186
DOI: 10.1305/NDJFL/1093635001
description: scientific article; zbMATH DE number 4154414