Abstract

We specialise Aronszajn trees by an $\omega ^\omega $ -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 "◇∂ and every Aronszajn tree is special" is consistent relative to ZFC