Journal of Symbolic Logic

The club principle and the distributivity number

Heike Mildenberger

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We give an affirmative answer to Brendle's and Hrušák's question of whether the club principle together with 𝔥 > ℵ1 is consistent. We work with a class of axiom A forcings with countable conditions such that q≥n p is determined by finitely many elements in the conditions p and q and that all strengthenings of a condition are subsets, and replace many names by actual sets. There are two types of technique: one for tree-like forcings and one for forcings with creatures that are translated into trees. Both lead to new models of the club principle.

Article information

J. Symbolic Logic, Volume 76, Issue 1 (2011), 34-46.

First available in Project Euclid: 4 January 2011

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E15: Descriptive set theory [See also 28A05, 54H05] 03E17: Cardinal characteristics of the continuum 03E35: Consistency and independence results

Ostaszewski club axiom A forcing cardinal characteristics


Mildenberger, Heike. The club principle and the distributivity number. J. Symbolic Logic 76 (2011), no. 1, 34--46. doi:10.2178/jsl/1294170988.

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