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