MacNeille completions and canonical extensions

  • Gehrke M
  • Harding J
  • Venema Y
37Citations
Citations of this article
14Readers
Mendeley users who have this article in their library.

Abstract

Let V V be a variety of monotone bounded lattice expansions, that is, bounded lattices endowed with additional operations, each of which is order preserving or reversing in each coordinate. We prove that if V 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 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.

References Powered by Scopus

Partially ordered sets

221Citations
N/AReaders
Get full text

Varieties of complex algebras

192Citations
N/AReaders
Get full text

Bounded lattice expansions

151Citations
N/AReaders
Get full text

Cited by Powered by Scopus

Generalized kripke frames

62Citations
N/AReaders
Get full text

Algebraic proof theory for substructural logics: Cut-elimination and completions

58Citations
N/AReaders
Get full text

MacNeille completions of lattice expansions

23Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Gehrke, M., Harding, J., & Venema, Y. (2005). MacNeille completions and canonical extensions. Transactions of the American Mathematical Society, 358(2), 573–590. https://doi.org/10.1090/s0002-9947-05-03816-x

Readers' Seniority

Tooltip

Professor / Associate Prof. 5

45%

Researcher 5

45%

PhD / Post grad / Masters / Doc 1

9%

Readers' Discipline

Tooltip

Mathematics 7

58%

Computer Science 3

25%

Physics and Astronomy 1

8%

Psychology 1

8%

Save time finding and organizing research with Mendeley

Sign up for free