The Boolean space of higher level orderings
Let K be an ordered field. The set X(K) of its orderings can be topologized to make it a Boolean space. Moreover, it has been shown by Craven that for any Boolean space Y there exists a field K such that X(K) is homeomorphic to Y. Becker's higher level ordering is a generalization of the usual concept of ordering. In a similar way to the case of ordinary orderings one can define a topology on the space of orderings of fixed exact level. We show that it need not be Boolean. However, our main theorem...