Abstract
Nash-Williams showed that the collection of locally finite trees under the topological minor relation results in a well-quasi-order. As a consequence, Matthiesen proved that the number λ of topological types of locally finite tree must be uncountable. Since ℵ1≤λ≤c, finding the exact value of λ becomes non-trivial in the absence of the Continuum Hypothesis. In this paper we address this task by showing that λ=ℵ1 for locally finite trees with countably many rays. We also partially extend this result to locally finite trees with uncountably many rays.
Original language | English |
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Pages (from-to) | 243-259 |
Number of pages | 17 |
Journal | Fundamenta Mathematicae |
Volume | 256 |
Issue number | 3 |
DOIs | |
Publication status | Published - 6 Oct 2021 |