Creatures on ω1 and weak diamonds

Abstract

We specialise Aronszajn trees by an ω^ω-bounding forcing that adds reals. We work with creature forcings on uncountable spaces.

As an application of these notions of forcing, we answer a question of Moore, Hrušák and Džamonja whether ♢(𝔟) implies the existence of a Souslin tree in a negative way by showing that “♢(𝔡) and every Aronszajn tree is special” is consistent relative to ZFC.