A Large Pairwise Far Family of Aronszajn Trees

TL;DR

This paper constructs a large family of complex Aronszajn trees with specific properties, using advanced set-theoretic principles, expanding understanding of tree structures in set theory.

Contribution

It introduces a new large family of Aronszajn trees with unique embedding and non-special properties via the proxy principle, advancing the theory of such trees.

Findings

Constructed a large family of Aronszajn trees with specific properties

Demonstrated the non-existence of club isomorphic subtrees in these trees

Utilized the proxy principle of Brodsky-Rinot in the construction

Abstract

We construct a large family of normal $\kappa$-complete $\mathbb{R}_\kappa$-embeddable non-special $\kappa^+$-Aronszajn trees which have no club isomorphic subtrees using an instance of the proxy principle of Brodsky-Rinot.