PP-2004-05: MacNeille completions and canonical extensions

PP-2004-05: Gehrke, Mai and Harding, John and Venema, Yde (2004) MacNeille completions and canonical extensions. [Report]

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Let $V$ be a variety of monotone bounded lattice expansions, that is,
lattices endowed with additional operations, each of which is order
preserving or reversing in each coordinate.
We prove that if $V$ is closed under MacNeille completions, then it is also
closed under canonical extensions.
As a corollary we show that in the case of Boolean algebras with operators,
any such variety $V$ is generated by an elementary class of relational

Our main technical construction reveals that the canonical extension of
a monotone bounded lattice expansion can be embedded in the MacNeille
completion of any sufficiently saturated elementary extension of the
original structure.

Item Type: Report
Report Nr: PP-2004-05
Series Name: Prepublication (PP) Series
Year: 2004
Uncontrolled Keywords: MacNeille completion, canonical extension, lattice ordered algebra, Boolean algebra with operators
Depositing User: Yde Venema
Date Deposited: 12 Oct 2016 14:36
Last Modified: 12 Oct 2016 14:36
URI: https://eprints.illc.uva.nl/id/eprint/116

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