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- W4300720232 abstract "Defining P* to be the complete lattice of upsets (ordered by reverse inclusion) of a poset P we give necessary and sufficient conditions on a subset S of P* for P to admit a meet-completion e from P to Q where e preserves the infimum of an upwardly closed set from P if and only if it is in S. We show that given S satisfying these conditions the set M of these completions forms a topped weakly lower semimodular lattice. In particular, when P is finite M is a lower semimodular lattice, and a lower bounded homomorphic image of a free lattice. We provide an example where M does not have a bottom element." @default.
- W4300720232 created "2022-10-04" @default.
- W4300720232 creator A5000606764 @default.
- W4300720232 date "2012-01-16" @default.
- W4300720232 modified "2023-09-26" @default.
- W4300720232 title "Preserving meets in meet-dense poset completions" @default.
- W4300720232 doi "https://doi.org/10.48550/arxiv.1201.3285" @default.
- W4300720232 hasPublicationYear "2012" @default.
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