Distributive Aronszajn trees
Ari Meir Brodsky, Assaf Rinot

TL;DR
This paper proves that under certain set-theoretic conditions, the existence of a special type of Aronszajn tree can be derived using a new approach involving walks on ordinals and club guessing, expanding understanding of square principles.
Contribution
It demonstrates that the existence of a normal λ-distributive λ^+-Aronszajn tree follows from a weaker square principle, using novel methods involving walks and club guessing.
Findings
Replaces ^*_ with (^+,{<}) in proving the existence of Aronszajn trees.
Introduces a new construction method using walks on ordinals and club guessing.
Shows that (^+,{<}) does not bound the order-type of clubs, unlike previous assumptions.
Abstract
Ben-David and Shelah proved that if is a singular strong-limit cardinal and , then entails the existence of a normal -distributive -Aronszajn tree. Here, it is proved that the same conclusion remains valid after replacing the hypothesis by . As does not impose a bound on the order-type of the witnessing clubs, our construction is necessarily different from that of Ben-David and Shelah, and instead uses walks on ordinals augmented with club guessing. A major component of this work is the study of postprocessing functions and their effect on square sequences. A byproduct of this study is the finding that for regular uncountable, entails the existence of a partition of into many fat sets.…
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