Some examples of lattice-orders in real closed fields
Many examples of compatible lattice orders are constructed on real closed subfields of the field of all generalized power series, with coefficients in \(\mathbb{R}\) and exponents in \(\mathbb{Q}\). They are associated to orders in \(\mathbb{Q}\) which make \(\mathbb{Q}\) into a tree. In turn, these orders on \(\mathbb{Q}\), are afforded by subgroups of \(\mathbb{Q}\). Moreover, these fields are henselian with respect to a natural valuation.
scientific article; zbMATH DE number 446293