Creatures on ω 1 and weak diamonds

Journal of Symbolic Logic 74 (1):1-16 (2009)
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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

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Citations of this work

Finding generic filters by playing games.Heike Mildenberger - 2010 - Archive for Mathematical Logic 49 (1):91-118.

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References found in this work

Iterated perfect-set forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.
The fine structure of the constructible hierarchy.R. Björn Jensen - 1972 - Annals of Mathematical Logic 4 (3):229.

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