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1 results

  • The club principle and the distributivity number

  • Heike Mildenberger
  • Journal:
    The Journal of Symbolic Logic / Volume 76 / Issue 1 / March 2011
    Published online by Cambridge University Press:
    12 March 2014, pp. 34-46
    Print publication:
    March 2011

  • 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.