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The results described here are partly contained in the author's doctoral thesis [15] which was partly supported by ONR Contract N00014-67-A-0298-0015.
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Markowsky, G. The representation of posets and lattices by sets. Algebra Universalis 11, 173–192 (1980). https://doi.org/10.1007/BF02483096
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DOI: https://doi.org/10.1007/BF02483096