University of Birmingham > Talks@bham > Topology and Dynamics seminar > Locally finite trees and the topological minor relation

## Locally finite trees and the topological minor relationAdd to your list(s) Download to your calendar using vCal - Dr. Jorge Bruno (University of Winchester)
- Thursday 25 April 2019, 13:00-14:00
- Lecture Room C, Watson Building.
If you have a question about this talk, please contact Tony Samuel. Nash-Williams showed that the collection of locally finite trees under the topological minor relation results in a BQO (better-quasi-order). Naturally, two interesting questions arise: 1. What is the number \lambda of topological types of locally finite trees? 2. What are the possible sizes of an equivalence class of locally finite trees? For (1), clearly, \omega_0 \leq \lambda \leq c and Matthiesen refined it to \omega_1 \leq \lambda \leq c. Thus, this question becomes non-trivial in the absence of the Continuum Hypothesis. In this talk we address both questions by showing – entirely within ZFC - that for a large collection of locally finite trees that includes those with countably many rays: - \lambda = \omega_1, and - the size of an equivalence class can only be either 1 or c. This talk is part of the Topology and Dynamics seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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