## Abstract We characterize complete Boolean algebras with dense subtrees. The main results show that a complete Boolean algebra contains a dense tree if its generic filter collapses the algebra's density to its distributivity number and the reverse holds for homogeneous algebras. (© 2006 WILEY‐VCH
Completing Boolean Algebras by Nonstandard Methods
✍ Scribed by Jürg Schmid
- Publisher
- John Wiley and Sons
- Year
- 1974
- Tongue
- English
- Weight
- 150 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0044-3050
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📜 SIMILAR VOLUMES
The notion of a BooLEan algebra with operators was introduced by J~NSSON and TARSKI [ 5 ] . It encompasses as special cases relation algebras (TARSKI [9]), closure algebras (MCKINSEY-TARSKI [S]), cylindric algebras (HENRIN-TARSKI [4]), polyadic algebras (HALMOS [Z]), and other algebras which have be
Lct 1 be an infinite cardinal and let A , B be Boolean algebras. A homomorphism h: , 4 4 B is said to be A-cmpkte if whenever X is a subset of A of cardinality I such that the join V X of X exists in A , then V h[X] exists in B and is equal to h(V X ) . If x is an infinite cardinal, B is said to be