Aronszajn trees and maximality -- Part 2

Abstract: Assuming the consistency of a weakly compact cardinal above a regular uncountable cardinal $\mu$, we prove the consistency of the existence of a wide $\mu<sup>+$-Aronszajn tree, i.e. a tree of height and cardinality $\mu<sup>+$ with no branches of length $\mu<sup>+$, into which every wide $\mu<sup>+$-Aronszajn tree can be embedded.