The Boolean space of higher level orderings

• Autorzy: Katarzyna Osiak
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 12D15: Fields related with sums of squares (formally real fields, Pythagorean fields, etc.)
• 13J30: Real algebra

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2007
• Tom: 196
• Numer: 2
• Strony: 101-117

Daty

wydano

2007

Twórcy

autor

Katarzyna Osiak

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Identyfikatory

DOI

10.4064/fm196-2-1