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 says that for any n and any Boolean space Y there exists a field, the space of orderings of fixed exact level n of which is homeomorphic to Y.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm196-2-1,
author = {Katarzyna Osiak},
title = {The Boolean space of higher level orderings},
journal = {Fundamenta Mathematicae},
volume = {193},
year = {2007},
pages = {101-117},
zbl = {1126.12002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm196-2-1}
}
Katarzyna Osiak. The Boolean space of higher level orderings. Fundamenta Mathematicae, Tome 193 (2007) pp. 101-117. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm196-2-1/