Proper cuts in \(^*R\)
type: Item
instance of: scholarly article
title: Proper cuts in \(^*R\)
zbMATH Open document ID: 0884.03061
author: Benjamin Delay
published in: Annales Mathématiques Blaise Pascal
publication date: 1998-03-17T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/79176
review text: The paper deals with various methods of constructing nonstandard models in which \(^{\ast}{ }R\) is Scott complete as well as models in which it is incomplete. The paper includes methods of S. Kamo, M. Forti and F. Honsell, H. J. Keisler and J. H. Schmerl [\textit{H. J. Keisler} and \textit{J. H. Schmerl}, ``Making the hyperreal line both saturated and complete'', J. Symb. Logic 56, No. 3, 1016-1025 (1991; Zbl 0747.03032)]. An ordered field \(K\) is called Scott complete if for every cut \((X,Y)\) in \(K\) such that \[ {\forall} {\epsilon{\in K}}{\:}({\epsilon}>0){\:}{\exists x}{\in X} {\:}{\exists y}{\in Y}{\:}(y-x{<\epsilon}) \] there exists a maximal element in \(X\) or a minimal element in \(Y\).
Mathematics Subject Classification ID: 03H05
Mathematics Subject Classification ID: 12L15
Mathematics Subject Classification ID: 12J15
Mathematics Subject Classification ID: 26E35
zbMATH DE Number: 1053374
zbMATH Keywords: nonstandard model
zbMATH Keywords: ordered field
zbMATH Keywords: Scott complete field
MaRDI profile type: Publication
OpenAlex ID: W2312773977
cites work: Nonstandard natural number systems and nonstandard models
cites work: Non-standard real number systems with regular gaps
cites work: Q3773884
cites work: Model theory.
cites work: Making the hyperreal line both saturated and complete
DOI: 10.5802/AMBP.84
description: scientific article; zbMATH DE number 1053374