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arXiv · 2510.26419

The power of trees

Ari Meir Brodsky·Assaf Rinot·Shira Yadai
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Abstract

We give two consistent constructions of trees $T$ whose finite power $T^{n+1}$ is sharply different from $T^n$: 1. An $\aleph_1$-tree $T$ whose interval topology $X_T$ is perfectly normal, but $(X_T)^2$ is not even countably metacompact. 2. For an inaccessible $\kappa$ and a positive integer $n$, a $\kappa$-tree such that all of its $n$-derived trees are Souslin and all of its $(n+1)$-derived trees are special.

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Ari Meir Brodsky, Assaf Rinot, Shira Yadai. 2025-10-30. The power of trees. https://doi.org/10.1016/j.apal.2026.103776

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