The club principle and the distributivity number

Abstract. We give an affirmative answer to Brendle’s and Hruˇs´ak’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.

• Type: Journal
• Year: 2011
• Where: JSYML
• Authors: Heike Mildenberger
• Keywords: Affirmative Answer, Club Principle, JSYML 2011, Tree-like Forcings