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
Duffus, D. and Goddard, T. (1996) Products of chains with monochromatic maximal chains and antichains, Order 13, 101–117.
Duffus, D., Rodl, V., Sauer, N., and Woodrow, R.E. (1992) Coloring ordered sets to avoid monochromatic maximal chains, Canad. J. Math. 44(1), 91–103.
Jech, T. (1978) Set Theory, Academic Press, San Diego.
Milner, E. C. and Pouzet, M. (1982) On the cofinality of partially ordered sets, in I. Rival (ed.), Ordered Sets, D. Reidel Publishing Co., Dordrecht, pp. 279–298.
Rosenstein, J. G. (1982) Linear Orderings, Academic Press, San Diego.
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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