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Bases of countable Boolean algebras

Published online by Cambridge University Press:  12 March 2014

R. S. Pierce
R. S. Pierce*
Affiliation:
University of Hawaii, Honolulu, Hawaii 96822
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Extract

The purpose of this note is to give a short proof of a conjecture of Feiner that every countable Boolean algebra has an ordered basis that is a lexicographic sum of well-ordered sets over the ordered set η of all rational numbers. Actually, we prove a slightly more precise fact, which is formulated below as Theorem 3. An earlier proof of Feiner's conjecture was obtained by David Cossack (unpublished), using a different method.

Our proof will use the following property of Cantor's dyadic discontinuum D.

Information

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 38 , Issue 2 , June 1973 , pp. 212 - 214
Copyright
Copyright © Association for Symbolic Logic 1973

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References

REFERENCES

[1]Mayer, R. D. and Pierce, R. S., Boolean algebras with ordered bases, Pacific Journal of Mathematics, vol. 10 (1960), pp. 925–942.CrossRefGoogle Scholar
[2]Pierce, R. S., Existence and uniqueness theorems for extensions of zero-dimensional compact metric spaces, Transactions of the American Mathematical Society, vol. 148 (1970), pp. 1–21.CrossRefGoogle Scholar
[3]Reichbach, M., A note on 0-dimensional compact sets, Bulletin of the Research Council of Israel, Section F (Mathematics and Physics), vol. 7F (1958), pp. 117–122.Google Scholar