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The club principle and the distributivity number

Published online by Cambridge University Press:  12 March 2014

Heike Mildenberger
Heike Mildenberger*
Affiliation:
Einstein Institute or Mathematics, The Hebrew University, Edmond Safra Campus Givat Ram, Jerusalem 91904, Israel, E-mail: heike@math.huji.ac.il
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Abstract

We give an affirmative answer to Brendle's and Hrušák's question of whether the club principle together with is consistent. We work with a class of axiom A forcings with countable conditions such that 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.

Keywords

Ostaszewski clubaxiom A forcingcardinal characteristics
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 1 , March 2011 , pp. 34 - 46
Copyright
Copyright © Association for Symbolic Logic 2011

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