A note on Jónsson's theorem
type: Item
instance of: scholarly article
title: A note on Jónsson's theorem
zbMATH Open document ID: 0656.03020
DOI: 10.1007/BF01229985
published in: Algebra Universalis
publication date: 1988-01-01T00:00:00Z
review text: The author presents a model-theoretic proof of Jónsson's Theorem. Considering a type of algebras which have distributive lattices of congruences he proves that for any class of algebras \({\mathcal K}\) every subdirectly irreducible member \({\mathcal A}\) of the variety generated by \({\mathcal K}\) is a homomorphic image of a subalgebra of an ultraproduct of algebras in \({\mathcal K}\). The main step is to show that \({\mathcal A}\) is a model of the positive universal theory of \({\mathcal K}\).
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 08B10
zbMATH DE Number: 4070872
zbMATH Keywords: equational theory
zbMATH Keywords: subdirectly irreducible algebra
zbMATH Keywords: model-theoretic proof of Jónsson's Theorem
author: Johan van Benthem
reviewed by: Oleg Belegradek
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01229985
OpenAlex ID: W2323056857
description: scientific article; zbMATH DE number 4070872