, Volume 32, Issue 3, pp 379–386 | Cite as

Character of Pseudo-Tree Algebras



For any Boolean algebra A, the character of A is χ(A)= min{κ: every ultrafilter on A can be generated by at most κ elements}. A pseudo-tree is a partial order (T,≤ T ) such that for every t in T, the set {sT:s T t} is a linear order. The pseudo-tree algebra on T, denoted Treealg T, is the subalgebra of \(\mathcal {P}(T)\) generated by the cones {sT:s T t}, for t in T. Ultrafilters on a pseudo-tree algebra Treealg T are in one-to-one correspondence with initial chains of T whenever T has a least element. We give an explicit description of a generating set of the ultrafilter corresponding to a given initial chain, and we use this to describe the character of Treealg T in terms of the structure of initial chains of T.


Character Pseudo-tree Pseudo-tree algebra Ultrafilter 


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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.California State University Channel IslandsCamarilloUSA

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