On finite models of regular identities
type: Item
instance of: scholarly article
title: On finite models of regular identities
zbMATH Open document ID: 0694.03025
author: Józef Dudek
author: Andrzej Kisielewicz
published in: Notre Dame Journal of Formal Logic
publication date: 1989-01-01T00:00:00Z
review text: A regular identity is one where the same variables appear on both sides of \(=\). For each finite type \(\tau\) of algebras and each set A with a semilattice operation one can define a \(\tau\)-semilattice on A. \(\tau\)- semilattices are ``trivial'' models of regular identities. The authors give a finite set of regular identities \(\Sigma\) such that each finite model of \(\Sigma\) is a \(<2,2>\)-semilattice and such that \(\Sigma\) has a model which is not a \(<2,2>\)-semilattice. They also show that a single regular identity has a nontrivial finite model (not a \(\tau\)- semilattice).
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 03C13
zbMATH DE Number: 4135925
zbMATH Keywords: finite type of algebras
zbMATH Keywords: semilattice
zbMATH Keywords: models of regular identities
reviewed by: J. M. Plotkin
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1305/ndjfl/1093635244
OpenAlex ID: W2083077037
DOI: 10.1305/NDJFL/1093635244
description: scientific article; zbMATH DE number 4135925