Displaying similar documents to “Boolean Vector Space. III.”

The Boolean space of higher level orderings

Katarzyna Osiak (2007)

Fundamenta Mathematicae

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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...

On Boolean modus ponens.

Sergiu Rudeanu (1998)

Mathware and Soft Computing

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An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].