Abstract
Davis and Bolz (1974) considered, and to some extent classified, compatible tight Riesz order on the group of all order-preserving permutations of a totally ordered field. Glass (1976) carried out a more general study of compatible tight Riesz orders on ordered permutation groups and, in particular, showed the importance of determining compatible tight Riesz orders on O-primitive ordered permutation groups. However, the general problems of existence and classification of compatible tight Riesz orders on O-primitive ordered permutation groups remained open.
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