Homogenizable relational structures
type: Item
instance of: scholarly article
title: Homogenizable relational structures
zbMATH Open document ID: 0706.03030
author: Jacinta Covington
published in: Illinois Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: A class \({\mathcal C}\) of structures has the local failure of amalgamation iff there are in \({\mathcal C}\) finitely many diagrams \({\mathcal D}_ j\) such that any diagram \({\mathcal D}\) in \({\mathcal C}\) fails to be amalgamated in \({\mathcal C}\) iff one of the \({\mathcal D}_ j's\) is embeddable in \({\mathcal D}\). Then the author proves: Let \({\mathcal L}\) be a purely relational languages. Let \(\Sigma\) be a set of universal \({\mathcal L}\)-sentences. Let \({\mathcal C}\) be the class of models of \(\Sigma\). Assume that the class of finite \({\mathcal C}\)-structures satisfies the Joint Embedding Property and that it has Local Failure of Amalgamation. Then \({\mathcal C}\) is homogenizable. It is shown further that the theory of these ``homogenized'' structures is model complete.
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 03C52
zbMATH DE Number: 4158612
zbMATH Keywords: homogenizable structures
zbMATH Keywords: model completeness
zbMATH Keywords: local failure of amalgamation
zbMATH Keywords: purely relational languages
reviewed by: F. G. Asenjo
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4158612