Abstract
The following theorem is proved: Letc be an infinite cardinal. There exists a partially ordered set of cardinalc, which contains no infinite independent subset, and which is not decomposable into less thanc chains.
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Dilworth, R. P., 1950, A decomposition theorem for partially ordered sets,Ann. of Math.,51, 161–166.
Perles, M. A., 1963, A proof of Dilworth’s decomposition theorem for partially ordered sets,Israel Jour. Math.,1, 105.
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Peles, M.A. On dilworth’s theorem in the in finite case. Israel J. Math. 1, 108–109 (1963). https://doi.org/10.1007/BF02759806
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DOI: https://doi.org/10.1007/BF02759806