Please use this identifier to cite or link to this item:

Title: Axiomatics for the externa lnumbers of nonstandardanalysis
Authors: Dinis, Bruno
van den Berg, Imme
Editors: Ross, David
Keywords: External numbers
nonstandard analysis
complete arithmetical solids
Issue Date: Dec-2017
Publisher: Journal of Logic and Analysis
Citation: Bruno Dinis, Axiomatics for the externa lnumbers of nonstandardanalysis Imme van den Berg, Journal of Logic & Analysis 9:7 (2017) 1–47 ISSN 1759-9008
Abstract: Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix. Due to the stability by some shifts, externa lnumbers may be seen as mathematical models for orders of magnitude. The algebraic properties of external numbers gave rise to the so-called solids, which are extensions of ordered fields, having a restricted distributivity law. However, necessary and sufficient conditions can be given for distributivity to hold. In this article we develop an axiomatics for the external numbers. The axioms are similar to, but mostly somewhat weaker than the axioms for the real numbers and deal with algebraic rules, Dedekind completeness and the Archimedean property. A structure satisfying these axioms is called a complete arithmetical solid. We show that the external numbers form a complete arithmetic alsolid, implying the consistency of th eaxioms presented. We also show that the set of precise elements (elements with minimal magnitude) has abuilt-in nonstandard model of the rationals. Indeed the set of precise elements is situated between the nonstandard rationals and the nonstandard reals whereas the set of non-precise numbers is completely determined.
Type: article
Appears in Collections:CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica

Files in This Item:

File Description SizeFormat
Journal of Logic and Analysis 308-1037-1-PB (1).pdf540.07 kBAdobe PDFView/Open
FacebookTwitterDeliciousLinkedInDiggGoogle BookmarksMySpaceOrkut
Formato BibTex mendeley Endnote Logotipo do DeGóis 

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.


Dspace Dspace
DSpace Software, version 1.6.2 Copyright © 2002-2008 MIT and Hewlett-Packard - Feedback
UEvora B-On Curriculum DeGois