Algebra universalis

, 61:151 | Cite as

Algebraically expandable classes

Article

Abstract

An algebraically expandable class is a class of similar algebras axiomatizable by sentences of the form \({(\forall\exists ! \bigwedge eq)}\) . The problem investigated in this work is that of finding all algebraically expandable classes within a given variety. A complete solution is presented for a number of varieties, including the classes of Boolean algebras, Stone algebras, semilattices, distributive lattices and generalized Kleene algebras. We also study the problem for the case of discriminator varieties, where we prove that there is a lattice isomorphism between the lattice of all algebraically expandable classes of the variety and a certain lattice of subclasses of the simple members of the variety. Finally this connection is applied to calculating the algebraically expandable subclasses of the varieties of monadic algebras and P-algebras.

2000 Mathematics Subject Classification

08C10 08B10 03C40 06D30 

Keywords and phrases

Kleene algebra discriminator variety function definition sentence 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Facultad de Matemáteca, Astronomía y FíisicaUniversidad Nacional de CórdobaCórdobaArgentina

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