Cellularity of Pseudo-Tree Algebras
Brown, Jennifer
Notre Dame J. Formal Logic, Tome 47 (2006) no. 1, p. 353-359 / Harvested from Project Euclid
Recall that for any Boolean algebra (BA) A, the cellularity of A is c(A) = sup{|X| : X is a pairwise-disjoint subset of A}. A pseudo-tree is a partially ordered set (T, ≤) such that for every t in T, the set {r ∊ T : r ≤ t} is a linear order. The pseudo-tree algebra on T, denoted Treealg(T), is the subalgebra of ℘(T) generated by the cones {r ∊ T : r ≥ t}, for t in T. We characterize the cellularity of pseudo-tree algebras in terms of cardinal functions on the underlying pseudo-trees. For T a pseudo-tree, c(Treealg(T)) is the maximum of four cardinals c\sbT, ι\sbT, φ\sbT, and μ\sbT : roughly, c\sbT measures the "tallness" of the pseudo-tree T; ι\sbT the "breadth"; φ\sbT the number of "finite branchings"; and μ\sbT the number of places where T "does not branch." We give examples to demonstrate that all four of these cardinals are needed.
Publié le : 2006-07-14
Classification:  cellularity,  pseudo-tree,  pseudo-tree algebra,  06E05,  06E99
@article{1163775442,
     author = {Brown, Jennifer},
     title = {Cellularity of Pseudo-Tree Algebras},
     journal = {Notre Dame J. Formal Logic},
     volume = {47},
     number = {1},
     year = {2006},
     pages = { 353-359},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1163775442}
}
Brown, Jennifer. Cellularity of Pseudo-Tree Algebras. Notre Dame J. Formal Logic, Tome 47 (2006) no. 1, pp.  353-359. http://gdmltest.u-ga.fr/item/1163775442/