Journal of Symbolic Logic

Creatures on ω1 and weak diamonds

Heike Mildenberger

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Abstract

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

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

Dates
First available in Project Euclid: 4 January 2009

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1231082299

Digital Object Identifier
doi:10.2178/jsl/1231082299

Mathematical Reviews number (MathSciNet)
MR2499417

Zentralblatt MATH identifier
1193.03075

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

Citation

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


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