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Compatible tight Riesz orders on ordered permutation groups

Published online by Cambridge University Press:  09 April 2009

G. Davis  and
E. Loci
G. Davis
Affiliation:
Department of Mathematics, La Trobe University, Victoria, 3083, Australia.
E. Loci
Affiliation:
Department of Mathematics, La Trobe University, Victoria, 3083, Australia.
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Abstract

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The pointwise order makes the group A(Ω) of order-preserving permutations of a totally-ordered set Ω a lattice-ordered group. We give some criteria for determining the compatible tight Riesz orders on A(Ω) in the case of Ω being a totally-ordered field, and then obtain various adjunctionshellip one between tight Riesz orders on A(Ω) and certain ideals of the fixed point lattice Φ(Ω), and a second between maximal tangents and certain filters of Φ(Ω). We also establish a correspondence between tight Riesz orders and first-order properties. Finally, we make use of our results to say what we can in the case of the automorphisms of the real field, and to pose several open problems.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 3 , May 1976 , pp. 317 - 333
Copyright
Copyright © Australian Mathematical Society 1976

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