Clones on three elements preserving a binary relation
type: Item
instance of: scholarly article
title: Clones on three elements preserving a binary relation
zbMATH Open document ID: 1115.08004
author: Anne Fearnley
published in: Algebra Universalis
publication date: 2007-04-02T00:00:00Z
review text: A clone on a set \(X\) is a set of finitary operations on \(X\) which contains all projections and which is closed under composition. For finite \(X\), every clone is of the form \(\text{Pol}(R)\), where \(R\) is a set of finitary relations on \(X\), and \(\text{Pol}(R)\) is the set of all operations which preserve all \(r\in R\). In particular, every clone is an intersection of clones which can be represented as sets of operations preserving a single finitary relation on \(X\), i.e. of clones of the form \(\text{Pol}(\{r\})\). In her Master's thesis (Université de Montréal 1992), the author of the present paper described all clones on a three-element set which are of the form \(\text{Pol}(\{r\})\) for a binary relation \(r\). There are 266 such clones. This paper is essentially a summary of the thesis.
reviewed by: Michael Pinsker
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 5139581
zbMATH Keywords: clone
zbMATH Keywords: polymorphism
zbMATH Keywords: three-valued logic
MaRDI profile type: Publication
full work available at URL: s00012-007-1985-5
OpenAlex ID: W2022964014
DOI: 10.1007/S00012-007-1985-5
description: scientific article; zbMATH DE number 5139581