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Obstacles to Extending Mirsky's Theorem

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Abstract

For each infinite cardinal κ, there is a locally finite poset which has no infinite chains and which cannot be covered by κ antichains.

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References

  1. Dilworth, R. P. (1960) A decomposition theorem for partially ordered sets, Ann. of Math. 51, 161–166.

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  2. Mirsky, L. (1971) A dual to Dilworth's decomposition theorem, Amer. Math. Monthly 78, 876–877.

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  3. Perles, M. A. (1963) On Dilworth's theorem in the infinite case, Israel J. Math. 1, 108–109.

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  4. Spiegel, E. and O'Donnell, C. J. (1997) Incidence Algebras, Monographs Textbooks Pure Appl. Math. 206, Marcel Dekker, New York.

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Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, CT, 06269-3009, U.S.A.

    James H. Schmerl

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  1. James H. Schmerl
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Schmerl, J.H. Obstacles to Extending Mirsky's Theorem. Order 19, 209–211 (2002). https://doi.org/10.1023/A:1016541101728

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  • DOI: https://doi.org/10.1023/A:1016541101728

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