Geodesic
Weakly Homogeneous Order Types
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 159-161

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An order type α is said to be weakly homogeneous (א0 homogeneous) if for any x1 < x2 and y1 < y2 there exists an order preserving bijection f on α such that f(xi)= y i for i = 1, 2. The reverse of an order type a is denoted, as usual, by α*. We say that α is order invertible if α*≤α. J. Q. Longyear [5] has asked whether for a weakly homogeneous order type α such that no (non-trivial) interval of α is order invertible we may deduce that every interval of α contains a copy of ηω1 or (ηω1)*. 
Adams, M. E. Weakly Homogeneous Order Types. Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 159-161. doi: 10.4153/CMB-1975-032-2
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     title = {Weakly {Homogeneous} {Order} {Types}},
     journal = {Canadian mathematical bulletin},
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     year = {1975},
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     number = {2},
     doi = {10.4153/CMB-1975-032-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-032-2/}
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