Cardinality, saturation and finiteness
type: Item
instance of: scholarly article
title: Cardinality, saturation and finiteness
zbMATH Open document ID: 0880.03018
author: Philippe Veschambre
published in: Annales Mathématiques Blaise Pascal
publication date: 1998-01-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/79174
review text: The author uses some results of J. Keisler and M. Benda to investigate relations between such properties of a model as its cardinality and saturation. Let \( {\mathcal M}\) be a model and \( ^{\ast}{ }{\mathcal M} \) be an extension of \({\mathcal M}\). Consistency of ZFC is supposed. Let be \( M\in{\mathcal M} \), \(\alpha\) be a cardinal. Denote by \(F_{\alpha}(M)\) the set of filters in \(M\). The set \(^{\ast}{ }M\) is said to be \({\alpha}\)-regular iff \({\forall}F{\in}F_{\alpha}(M)\:\:\)Monad\((F) \neq \emptyset\). Theorem 1 states that \(^{\ast}{ }M\) is \({\alpha}\)-regular iff \({\alpha}\) belongs to a hyperfinite internal set. The author mentions in the preface Theorem 2 but this is missing in the paper.
Mathematics Subject Classification ID: 03C50
Mathematics Subject Classification ID: 03C20
Mathematics Subject Classification ID: 03H05
zbMATH DE Number: 1053382
zbMATH Keywords: Saturation
zbMATH Keywords: regularity
zbMATH Keywords: ultrapower
zbMATH Keywords: internal
zbMATH Keywords: hyperfinite
MaRDI profile type: Publication
OpenAlex ID: W2320113468
cites work: On reduced products and filters
cites work: On cardinalities of ultraproducts
cites work: Ultraproducts of finite sets
cites work: A result concerning cardinalities of ultraproducts
DOI: 10.5802/AMBP.92
description: scientific article; zbMATH DE number 1053382