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Weakly Homogeneous Order Types

Published online by Cambridge University Press:  20 November 2018

M. E. Adams
M. E. Adams*
Affiliation:
University of Manitoba, Winnipeg, Canada
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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)*.

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 2 , June 1975 , pp. 159 - 161
Copyright
Copyright © Canadian Mathematical Society 1975

References

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