Oligomorphic clones
type: Item
instance of: scholarly article
title: Oligomorphic clones
zbMATH Open document ID: 1121.08005
author: Manuel Bodirsky
author: Hubie Chen
published in: Algebra Universalis
publication date: 2007-09-03T00:00:00Z
review text: A clone on a countable domain is called oligomorphic if its set of permutations forms an oligomorphic permutation group (that is, if it has finitely many orbits of finitary tuples). In this article the authors generalize some fundamental theorems of universal algebra from clones over a finite domain to oligomorphic clones. First, they define minimal oligomorphic clones, and present equivalent characterizations of minimality, and then generalize Rosenberg's five types classification to minimal oligomorphic clones. Also, they present a generalizations of the theorem of Baker and Pixley to oligomorphic clones.
Mathematics Subject Classification ID: 08A40
Mathematics Subject Classification ID: 03C05
Mathematics Subject Classification ID: 03C35
zbMATH DE Number: 5186255
zbMATH Keywords: \(\omega\)-categoricity
zbMATH Keywords: preservation theorems
zbMATH Keywords: oligomorphic permutation groups
zbMATH Keywords: clones on infinite domains
zbMATH Keywords: minimal locally closed clones
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: s00012-007-2026-0
OpenAlex ID: W4235890131
DOI: 10.1007/S00012-007-2026-0
description: scientific article; zbMATH DE number 5186255