Abstract
This problem is our starting point: Characterize those chains (linear orderings) C having a first and second element and with all principal final segments isomorphic to C. A description is obtained in the countable scattered case. For nonscattered countable chains, the problem is the same as the following: Characterize the colorings of the rational chain Q such that every open principal final segment of Q is color-isomorphic to Q.
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References
K. G. Johnston and P. R. Jones (1985) Modular inverse semigroups (preprint).
J. G. Rosenstein (1982) Linear Orderings, Academic Press, New York.
W. Sierpinski (1950) General Topology, University of Toronto Press, Toronto.
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Communicated by M. Pouzet
Supported by a NATO Grant for International Collaboration.
Supported by NSF Grant 8302054 and ONR Contract N00014-85-K-0769.
Supported by NSERC, Canada.
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Bonnet, R., Duffus, D. & Woodrow, R.E. Coloring chains. Order 6, 69–89 (1989). https://doi.org/10.1007/BF00341638
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DOI: https://doi.org/10.1007/BF00341638