Bases of countable Boolean algebras
- 1 June 1973
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 38 (2) , 212-214
- https://doi.org/10.2307/2272057
Abstract
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 An earlier proof of Feiner's conjecture was obtained by David Cossack (unpublished), using a different method.Our proof will use the following property of Cantor's dyadic discontinuum D.Keywords
This publication has 2 references indexed in Scilit:
- Existence and uniqueness theorems for extensions of zero-dimensional compact metric spacesTransactions of the American Mathematical Society, 1970
- Boolean algebras with ordered basesPacific Journal of Mathematics, 1960