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THE SMALL INDEX PROPERTY FOR COUNTABLE 1-TRANSITIVE LINEAR ORDERS

Published online by Cambridge University Press:  31 January 2005

K. CHICOT  and
J. K. TRUSS
K. CHICOT
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England e-mails: k.chicot@ri.ac.uk, pmtjkt@leeds.ac.uk
J. K. TRUSS
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England e-mails: k.chicot@ri.ac.uk, pmtjkt@leeds.ac.uk
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Abstract

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It is shown that the countable saturated discrete linear ordering has the small index property, but that the countable 1-transitive linear orders which contain a convex subset isomorphic to ${\Bbb Z}^2$ do not. Similar results are also proved in the coloured case.

Keywords

20B2706F15
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 47 , Issue 1 , January 2005 , pp. 69 - 75
Copyright
2005 Glasgow Mathematical Journal Trust