We specialise Aronszajn trees by an ωω-boundingforcing that adds reals. We work withcreature forcingson 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 treein a negative way by showing that“♢(𝔡) and every Aronszajn tree is special” is consistentrelative to ZFC.
"Creatures on ω1 and weak diamonds." J. Symbolic Logic 74 (1) 1 - 16, March 2009. https://doi.org/10.2178/jsl/1231082299