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An Ordered Set of Size ℵ1 with Monochromatic Maximal Chains

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Abstract

Every model of ZFC contains a product of two linear orders, each of size ℵ1, with the property that every subset or complement thereof contains a maximal chain.

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References

  1. Duffus, D. and Goddard, T. (1996) Products of chains with monochromatic maximal chains and antichains, Order 13, 101–117.

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  3. Jech, T. (1978) Set Theory, Academic Press, San Diego.

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Author information

Authors and Affiliations

  1. Mathematics and Computer Science Department, Emory University, Atlanta, Georgia, 30322, U.S.A.

    D. Duffus

  2. Mathematics and Computer Science Department, Emory University, Atlanta, Georgia, 30322, U.S.A.

    T. Goddard

Authors
  1. D. Duffus
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  2. T. Goddard
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Duffus, D., Goddard, T. An Ordered Set of Size ℵ1 with Monochromatic Maximal Chains. Order 17, 227–238 (2000). https://doi.org/10.1023/A:1026501224586

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  • DOI: https://doi.org/10.1023/A:1026501224586

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