Journal of Symbolic Logic

Creatures on ω1 and weak diamonds

Heike Mildenberger

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We specialise Aronszajn trees by an ωω-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.

Article information

J. Symbolic Logic, Volume 74, Issue 1 (2009), 1-16.

First available in Project Euclid: 4 January 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E35: Consistency and independence results 03E55: Large cardinals


Mildenberger, Heike. Creatures on ω 1 and weak diamonds. J. Symbolic Logic 74 (2009), no. 1, 1--16. doi:10.2178/jsl/1231082299.

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