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Q-ultrafilters and normal ultrafilters in B-algebras

✍ Scribed by Bronisław Tembrowski

Publisher
Springer Netherlands
Year
1986
Tongue
English
Weight
814 KB
Volume
45
Category
Article
ISSN
0039-3215

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✦ Synopsis

The firs~ par~ of the paper deals with some subclasses of B-algebras ~t~d Sheir applications to the semantics of SCI n, ~he Boolean s~rengthening of the sentential calculus with i~lentity (SCI). In the second part a generalization of the ~cKinsey-Tarski construction of well.connected topological Boolean algebras to the class of B-algebras is given.

and a, b-.aob is ~n addStional binary operation on A. Algebras of this kind, their rel.~tionships to some known classes of algebras as well as the theory of filters and congruences in B-algebras were investigated in [14]. Recall that ~ Boolean filter V is a Q-filter in d if a relation ~ (defined by a ~ b V g iff (aob)e V for every a, b cA) is a congruence of d compatible with V~ and V is a normal filter provided that ~ is the identity. B-algebras J-):EPARTMENT OF ~/~ATILEMA~IOS PEDAGOGICAL UNIVERSITY

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