Finite quasivarieties and self-referential conditions
type: Item
instance of: scholarly article
title: Finite quasivarieties and self-referential conditions
zbMATH Open document ID: 1105.08009
author: Alexei Vernitski
published in: Studia Logica
publication date: 2005-04-07T00:00:00Z
review text: The author considers classes of finite (universal) algebras defined by a system of quasi-identities, calling them `finite quasivarieties' or even `farieties'. He introduces a new type of formula, called `recursive quasi-identities', which are implications of the form \(\bigwedge_{1\leq i\leq n}\mathbf e_i\to\mathbf e\) where \(\mathbf e\) is a term equation and the \(\mathbf e_i\) are either term equations or so-called `positive recursive conditions'. The latter allow to express a certain degree of self-reference with the goal of simulating recursive definitions. The main result of the paper is that a class of finite algebras is a fariety if it can be defined by a system of recursive quasi-identities.
Mathematics Subject Classification ID: 08C15
zbMATH DE Number: 2153449
zbMATH Keywords: quasivariety
zbMATH Keywords: quasi-identity
zbMATH Keywords: pseudovariety
zbMATH Keywords: recursion
zbMATH Keywords: self-referential condition
MaRDI profile type: Publication
full work available at URL: s11225-005-7348-3
OpenAlex ID: W1963885651
cites work: Q4848740
cites work: On the membership problem for pseudovarieties of commutative semigroups
cites work: Pseudovarieties, generalized varieties and similarly described classes
cites work: Q4331824
cites work: Q3848243
cites work: Q5287508
cites work: Structure of lattices of varieties and lattices of quasivarieties: Similarity and difference. I
cites work: Q4220413
cites work: Algorithmic problems for finite groups and finite \(0\)-simple semigroups
cites work: Semigroups of order-preserving mappings
cites work: Q4548273
cites work: The semigroups of order-preserving mappings: quest for quasiidentities
cites work: Studying semigroups of mappings using quasi-identities
cites work: ON A CLASS OF SEMIGROUP PSEUDOVARIETIES WITHOUT FINITE PSEUDOIDENTITY BASIS
DOI: 10.1007/S11225-005-7348-3
description: scientific article; zbMATH DE number 2153449