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On the Representation of Boolean Algebras

Published online by Cambridge University Press:  20 November 2018

Günter Bruns
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Let B be a Boolean algebra and let ℳ and n be two systems of subsets of B, both containing all finite subsets of B. Let us assume further that the join ∨M of every set M∊ℳ and the meet ∧N of every set N∊n exist. Several authors have treated the question under which conditions there exists an isomorphism φ between B and a field δ of sets, satisfying the conditions:

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 5 , Issue 1 , January 1962 , pp. 37 - 41
Copyright
Copyright © Canadian Mathematical Society 1962

References

1 We denote by "∨, ∧" the lattice theoretical operations, by "∪, ∩" the corresponding set theoretical operations.

2 See Sikorski, Boolean algebras, Berlin-G?ttingen-Heidelberg 1960, pp. 79 ff and the literature cited there.

3 See Sikorski, loc. cit. p. 93, D).

4 See Sikorski, loc. cit., p. 80, 24. 1.