The club principle and the distributivity number

We give an affirmative answer to Brendle's and Hrušák's question of whether the club principle together with h > N₁ 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 t...

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Bibliographic Details
Published in:The Journal of symbolic logic 2011-03, Vol.76 (1), p.34-46
Main Author: Mildenberger, Heike
Format: Article
Language:English
Subjects:
03E15
03E17
03E35
axiom A forcing
Axioms
cardinal characteristics
Coordinate systems
Distributivity
Increasing sequences
Induced substructures
Logical theorems
Mathematical logic
Mathematical set theory
Mathematical sets
Mathematical theorems
Ostaszewski club
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Summary:We give an affirmative answer to Brendle's and Hrušák's question of whether the club principle together with h > N₁ 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.
ISSN:0022-4812
1943-5886
DOI:10.2178/jsl/1294170988