Cellularity of pseudo-tree algebras
by
Jennifer Horne
University of Colorado at Boulder

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_T, i_T, f_T, and m_T: roughly, c_T measures the "tallness" of the pseudo-tree T; i_T the "breadth"; f_T the number of "points of finite branching"; and m_T the number of "sections of no branching". This solves a problem posed by Monk in 1995: Describe cellularity for pseudo-tree algebras.

One may ask which of the 24 possible strict inequalities among these four cardinals are "attainable" by a pseudo-tree. (For example, is it consistent that there exists a pseudo-tree T such that f_T < m_T < c_T < i_T?) We will answer this question and briefly discuss our results on the relationship between attainment of various inequalities and the existence of k-Suslin trees.

Date received: February 27, 2005