Specializing Aronszajn trees and preserving certain weak diamonds
by Mildenberger and Shelah. [MdSh:848]
J Applied Analysis, 2009
We show that diamondsuit (R, L, not in)
together with ``all Aronszajn trees are special'' is consistent
relative to ZFC. The weak diamond for the uniformity of Lebegue null
sets was the only weak diamond in the Cichon diagramme for
relations whose consistency together with ``all Aronszajn trees are
special'' was not yet settled. We can have CH or 2^{aleph_0} =
aleph_2 . Our techniques give more on coverings by related small
sets that are preserved in iterations that are stronger relatives to
[Sh:f, Chap. V, sect. 5--7]
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