descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jun 2011Embargo end date: 01 Jan 2009 English Publisher:Elsevier BVJournal:Theoretical Computer Science, volume 412, pages 2,714-2,723 (issn: 0304-3975,

Authors: Gehrke, M.; Vosmaer, J.;

doi: 10.1016/j.tcs.2010.12.032 , 10.48550/arxiv.0909.0171

arXiv: 0909.0171

handle: https://repository.ubn.ru.nl/handle/2066/91616 , 11245/1.332372 , 2066/91616

Canonical extensions and canonicity via dcpo presentations

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Abstract

The canonical extension of a lattice is in an essential way a two-sided completion. Domain theory, on the contrary, is primarily concerned with one-sided completeness. In this paper, we show two things. Firstly, that the canonical extension of a lattice can be given an asymmetric description in two stages: a free co-directed meet completion, followed by a completion by \emph{selected} directed joins. Secondly, we show that the general techniques for dcpo presentations of dcpo algebras used in the second stage of the construction immediately give us the well-known canonicity result for bounded lattices with operators.

17 pages. Definition 5 was revised slightly, without changing any of the results

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Keywords

FOS: Computer and information sciences, Algebra and Topology, Computer Science - Logic in Computer Science, canonical extension, Lattice theory, Canonicity, 510, Lattices and duality, Theoretical Computer Science, Logic in Computer Science (cs.LO), Canonical extension, dcpo algebra, Continuous lattices and posets, applications, dcpo presentation, Complete lattices, completions, Algebra en Topologie, Computer Science(all)

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