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Cardinalities of infinite antichains in products of chains

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Abstract.

In response to a question of Ploščica and Haviar, a chain L is constructed such that \(L^3\) has an antichain of infinite cardinality \(\kappa\) while \(L^2\) does not. The construction applies to any singular \(\kappa\). (Independently, such chains have been constructed for certain regular \(\kappa\) by Goldstern and Shelah.)

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Authors and Affiliations

  1. Department of Mathematics Vanderbilt University Nashville, TN 37240 U.S.A., e-mail: farley@math.vanderbilt.edu, , , , , , , USA

    J.D. Farley

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  1. J.D. Farley
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Received January 18, 1999; accepted in final form July 6, 1999.

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Farley, J. Cardinalities of infinite antichains in products of chains. Algebra univers. 42, 235–238 (1999). https://doi.org/10.1007/s000120050136

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  • DOI: https://doi.org/10.1007/s000120050136

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