Abstract
It is shown that the dimension of a poset is the smallest cardinal number λ such that there is an embedding of the poset into a strict product of λ linear orders.
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References
HiraguchiTosio (1951) On the dimension of partially ordered sets, Sci. Rep. Kanazawa Univ. 1, 77–94. MR 17, p. 19.
DushnikB. & MillerE. W. (1941) Partially ordered sets, Amer. J. Math. 63, 600–610. MR 12 # 470.
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Communicated by D. Kelly
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Milner, E.C., Pouzet, M. A note on the dimension of a poset. Order 7, 101–102 (1990). https://doi.org/10.1007/BF00383178
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DOI: https://doi.org/10.1007/BF00383178