NDLI: MacNeille completions of lattice expansions

Content Provider	Springer Nature Link
Author	Theunissen, Mark Venema, Yde
Copyright Year	2007
Abstract	There are two natural ways to extend an arbitrary map between (the carriers of) two lattices, to a map between their MacNeille completions. In this paper we investigate which properties of lattice maps are preserved under these constructions, and for which kind of maps the two extensions coincide.Our perspective involves a number of topologies on lattice completions, including the Scott topologies and topologies that are induced by the original lattice. We provide a characterization of the MacNeille completion in terms of these induced topologies.We then turn to expansions of lattices with additional operations, and address the question of which equational properties of such lattice expansions are preserved under various types of MacNeille completions that can be defined for these algebras. For a number of cases, including modal algebras and residuated (ortho)lattice expansions, we provide reasonably sharp sufficient conditions on the syntactic shape of equations that guarantee preservation. Generally, our results show that the more residuation properties the primitive operations satisfy, the more equations are preserved.
Ending Page	193
Page Count	51
Starting Page	143
File Format	PDF
ISSN	00025240
e-ISSN	14208911
Journal	algebra universalis
Issue Number	2
Volume Number	57
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2007-09-18
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Boolean algebras with additional operations (diagonalizable algebras, etc.) Other algebras related to logic completions lattice-ordered algebras order topology Complete lattices, completions Topological lattices, order topologies MacNeille completions Algebra residuation modal algebras Sahlqvist theory Lattices and related structures ortholattices lattice expansions preservation results lattices Equational classes, universal algebra
Content Type	Text
Resource Type	Article
Subject	Logic Algebra and Number Theory

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Preservation of Sahlqvist fixed point equations in completions of relativized fixed point Boolean algebras with operators

MacNeille completion and profinite completion can coincide on finitely generated modal algebras

Topological duality and lattice expansions, II: Lattice expansions with quasioperators

Solvable covers of the boolean variety of unital ℓ-groups

More covers of the Boolean variety of unital ℓ-groups

Topo-canonical completions of closure algebras and Heyting algebras

Macneille completions of modal algebras john harding and guram bezhanishvili.

Topological duality and lattice expansions, I: A topological construction of canonical extensions

Codimension and pseudometric in co-Heyting algebras

MacNeille completions of lattice expansions

Similar Documents

Preservation of Sahlqvist fixed point equations in completions of relativized fixed point Boolean algebras with operators

MacNeille completion and profinite completion can coincide on finitely generated modal algebras

Topological duality and lattice expansions, II: Lattice expansions with quasioperators

Solvable covers of the boolean variety of unital ℓ-groups

More covers of the Boolean variety of unital ℓ-groups

Topo-canonical completions of closure algebras and Heyting algebras

Macneille completions of modal algebras john harding and guram bezhanishvili.

Topological duality and lattice expansions, I: A topological construction of canonical extensions

Codimension and pseudometric in co-Heyting algebras

MacNeille completions of lattice expansions