Countable embeddability skeletons of discriminator varieties
type: Item
instance of: scholarly article
title: Countable embeddability skeletons of discriminator varieties
zbMATH Open document ID: 0708.08005
DOI: 10.1007/BF01979200
published in: Algebra and Logic
publication date: 1989-01-01T00:00:00Z
review text: Let \({\mathbb{V}}\) be a variety of algebras. The set I\({\mathbb{V}}\) of isomorphism types of \({\mathbb{V}}\)-algebras together with the quasi-order \(\leq\) defined by the condition \(a\leq b\) iff any algebra of isomorphism type a can be embedded into some algebra of isomorphism type b, is called the embeddability skeleton of \({\mathbb{V}}\). The following theorem is proved: If \({\mathbb{V}}\) is a discriminator variety of finite signature which is not locally finite, then every countable partially ordered set can be isomorphically embedded into the skeleton of isomorphism types of countable algebras from \({\mathbb{V}}\).
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 06A06
zbMATH DE Number: 4162964
zbMATH Keywords: isomorphism types
zbMATH Keywords: quasi-order
zbMATH Keywords: embeddability skeleton
zbMATH Keywords: discriminator variety
author: A. G. Pinus
reviewed by: Ernest Płonka
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01979200
OpenAlex ID: W2053632134
description: scientific article; zbMATH DE number 4162964