The Boolean space of higher level orderings

Katarzyna Osiak. "The Boolean space of higher level orderings." Fundamenta Mathematicae 196.2 (2007): 101-117. <http://eudml.org/doc/282631>.

@article{KatarzynaOsiak2007,
abstract = {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.},
author = {Katarzyna Osiak},
journal = {Fundamenta Mathematicae},
keywords = {ordered field; ordering of higher level; signature; Boolean space},
language = {eng},
number = {2},
pages = {101-117},
title = {The Boolean space of higher level orderings},
url = {http://eudml.org/doc/282631},
volume = {196},
year = {2007},
}

TY - JOUR
AU - Katarzyna Osiak
TI - The Boolean space of higher level orderings
JO - Fundamenta Mathematicae
PY - 2007
VL - 196
IS - 2
SP - 101
EP - 117
AB - 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.
LA - eng
KW - ordered field; ordering of higher level; signature; Boolean space
UR - http://eudml.org/doc/282631
ER -