Abstract
A partial ordering on a set P can be weakened to an upper or lower semilattice ordering, respectively a lattice ordering, if and only if P is filtered in the appropriate direction(s).
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Marianne Delorme et Maurice Pouzet (1986?) Un théorème de Marc Krasner, de 1939, et ses rapports avec la comparaison des types de cofinalité, to appear in Actes du Jubilée Krasner.
Marc Krasner (1939) Un type d'ensembles semi-ordonnées et ses rapports avec une hypothése de M. A. Weil, Bull. Soc. Math. France, 67, 162–176.
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Communicated by G. Grätzer
This work was done while the author was partly supported by NSF contract DMS 85-02330.
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Bergman, G.M. Weakening partial orderings to lattice and semilattice orderings. Order 3, 283–286 (1986). https://doi.org/10.1007/BF00400291
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DOI: https://doi.org/10.1007/BF00400291