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Cellularity and the structure of pseudo-trees

Published online by Cambridge University Press:  12 March 2014

Jennifer Brown
Jennifer Brown*
Affiliation:
Department of Mathematics, Kenyon College, Ohio, USA. E-mail:brownja@member.ams.org
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Abstract

Let T be an infinite pseudo-tree. In [2], we showed that the cellularity of the pseudo-tree algebra Treealg(T) was the maximum of four cardinals cT, lT, ϕT, and μT: roughly, cT is the “tallness” of T: lT is the “width” of T, ϕ is the number of “points of finite branching” in T: and μ is the number of “sections of no branching” in T. Here we ask: which inequalities among these four cardinals may be satisfied, in some sense, by a pseudo-tree? We show that the possible inequalities among cT, lT, ϕT, and μT attained by pseudo-trees T are closely related to the existence of generalized Suslin trees.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 4 , December 2007 , pp. 1093 - 1107
Copyright
Copyright © Association for Symbolic Logic 2007

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References

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