Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-21T04:28:54.095Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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)*.

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

References

1. Dushnik, B. and Miller, E. W., Concerning similarity transformations of linearly ordered sets, Bull. Amer. Math. Soc. 46 (1940), 322-326.Google Scholar
2. Ginsburg, S., Some remarks on order types and decompositions of sets, Trans. Amer. Math. Soc. 74 (1953), 514-535.Google Scholar
3. Ginsburg, S., Further results on order types and decompositions of sets, Trans. Amer. Math. Soc. 77(1954), 122-150.Google Scholar
4. Ginsburg, S., Order types and similarity transformations, Trans. Amer. Math. Soc. 79 (1955), 341-361.Google Scholar
5. Longyear, J. Q., Patterns: the structure of linear homogeneous sets, preprint (see Notices Amer. Math. Soc. 21 (1974), A-293).Google Scholar
6. Rotman, B., On the comparison of order types, Acta Math. Sci. Hungar. 19 (1968), 311-327.Google Scholar