Universal wide Aronszajn tree
Siiri Kivim\"aki

TL;DR
This paper proves the consistency, under certain set-theoretic assumptions, of the existence of a universal wide Aronszajn tree that contains all such trees as subtrees.
Contribution
It demonstrates the relative consistency of a universal wide Aronszajn tree assuming a weakly compact cardinal.
Findings
Existence of a universal wide Aronszajn tree under set-theoretic assumptions.
The result relies on the consistency of a weakly compact cardinal.
Provides a new perspective on the structure of Aronszajn trees.
Abstract
A wide Aronszajn tree is a tree of size with no uncountable branches. Assuming the consistency of the existence of a weakly compact cardinal, we show the consistency of the existence of a wide Aronszajn tree that is \textit{universal} in the sense that it contains an isomorphic copy of every wide Aronszajn tree.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Logic, programming, and type systems · Computability, Logic, AI Algorithms
