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A proof of Dilworth’s decomposition theorem for partially ordered sets. (English) Zbl 0115.01702
References:
[1]de Bruijn N. G. and Erdös P. 1951, A colour problem for infinite graphs and, a problem in the theory of relations,Nederl. Akad. Wetensch. Proc. ser. A,54, 371–373.
[2]Dantzig G. B. and Hoffman, A. J., 1956, Dilworth’s theorem on partially orders sets, Linear inequalities and related systems,Annals of Mathematics Studies No. 38, Princeton University Press, pp. 207–214.
[3]Dilworth, R. P., 1950, A decomposition theorem for partially ordered sets,Ann. of Math. 51, 161–166. · Zbl 0038.02003 · doi:10.2307/1969503
[4]Fulkerson, D. R., 1956, Note on Dilworth’s decomposition theorem for partially ordered sets,Proc. Amer. Math. Soc.,7, 701–702.
[5]Gallai, T. and Milgram, A. N., 1960, Verallgemeinerung eines graphentheoretisch-Satzes von Rédei,Acta Sci. Math. (Szeged),21, 181–186.
[6]Gottschalk, W. H., 1951, Choice functions and Tychonoff’s theorem,Proc. Amer. Math. Soc.,2, 172.
[7]Halmos, P. R., and Vaughan, H. E., 1950, The marriage problem,Amer. J. Math.,72, 214–215. · Zbl 0034.29601 · doi:10.2307/2372148
[8]König, D., 1950,Theorie der endlichen und unendlichen Graphen, Chelsea Publishing Co., New York.
[9]Rado, R., 1949, Axiomatic treatment of rank in infinite sets,Canad. J. Math.,1, 337–343. · Zbl 0033.25302 · doi:10.4153/CJM-1949-031-1