Ordered fields with the dense orbits property
For a formally real field K let X(K) be the space of orderings. The automorphism group Aut(K) of K operates on X(K). K is said to have the 'dense orbits property' (DOP) if for all \(\alpha\in X(K)\) the orbit of \(\alpha\) is dense in X(K). The study of such fields, which was begun in \textit{D. W. Dubois} and the second author [Contemp. Math. 8, 265-288 (1982; Zbl 0484.12003)], is continued here. The main question considered is the behavior of the DOP under purely transcendental and under algebraic field extensions. Proposition 1.5 is false.
automorphisms acting on spaces of orderings
scientific article; zbMATH DE number 3845714