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 


  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.MATHMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1963

Authors and Affiliations

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

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