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Distributive Aronszajn trees
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. When contrasted with a
classic model of Magidor, this shows that it is equiconsistent with the
existence of a weakly compact cardinal that cannot be split into two
fat sets.Comment: 45 pages; improved and generalized some results, and streamlined the
presentatio