March 2008 Flat algebras and the translation of universal Horn logic to equational logic
Marcel Jackson
J. Symbolic Logic 73(1): 90-128 (March 2008). DOI: 10.2178/jsl/1208358744


We describe which subdirectly irreducible flat algebras arise in the variety generated by an arbitrary class of flat algebras with absorbing bottom element. This is used to give an elementary translation of the universal Horn logic of algebras, partial algebras, and more generally still, partial structures into the equational logic of conventional algebras. A number of examples and corollaries follow. For example, the problem of deciding which finite algebras of some fixed type have a finite basis for their quasi-identities is shown to be equivalent to the finite identity basis problem for the finite members of a finitely based variety with definable principal congruences.


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Marcel Jackson. "Flat algebras and the translation of universal Horn logic to equational logic." J. Symbolic Logic 73 (1) 90 - 128, March 2008.


Published: March 2008
First available in Project Euclid: 16 April 2008

zbMATH: 1141.03006
MathSciNet: MR2387934
Digital Object Identifier: 10.2178/jsl/1208358744

Primary: 03C05 , 06F99 , 08C15 , 20E10 , 20M18

Keywords: agreeable semigroup , Brandt semigroup , Clifford semigroup , flat algebra , flat extension of a group , flat semilattice , inverse semigroup , membership problems , Quasi-variety , Q-universal , the finite basis problem , undecidability , universal Horn class

Rights: Copyright © 2008 Association for Symbolic Logic


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Vol.73 • No. 1 • March 2008
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