Israel Journal of Mathematics

, Volume 1, Issue 2, pp 108–109 | Cite as

On dilworth’s theorem in the in finite case

  • Micha A. Peles


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.


Natural Number Group Theory Partial Order Distributive Lattice Order Relation 
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  1. 1.
    Dilworth, R. P., 1950, A decomposition theorem for partially ordered sets,Ann. of Math.,51, 161–166.CrossRefMathSciNetGoogle Scholar
  2. 2.
    Perles, M. A., 1963, A proof of Dilworth’s decomposition theorem for partially ordered sets,Israel Jour. Math.,1, 105.zbMATHMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1963

Authors and Affiliations

  • Micha A. Peles
    • 1
  1. 1.The Hebrew University of JerusalemIsrael

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