Journal of Symbolic Logic

The club principle and the distributivity number

Heike Mildenberger

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Abstract

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

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

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1294170988

Digital Object Identifier
doi:10.2178/jsl/1294170988

Mathematical Reviews number (MathSciNet)
MR2791336

Zentralblatt MATH identifier
1231.03040

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

Keywords
Ostaszewski club axiom A forcing cardinal characteristics

Citation

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


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