Adding clubs with square

We present a technique for destroying stationary subsets of P+ using partial square sequences. We combine this method with Gitik's poset for changing the cofinality of a cardinal without adding bounded sets to prove a variety of consistency results concerning saturated ideals and the set S(, +). In this paper we continue our study of consistency results concerning the set S(, + ) = {a P+ : o.t.(a) = (a )+ } from [5] and [6]. We present a method for destroying the stationarity of certain subsets of P+ , where is inaccessible, using partial square sequences. This method of destroying stationary sets has a variety of applications. We prove several results which support the general theme that the structure of S(, + ) can vary greatly depending on the particular model considered. For example, if is supercompact and

• Type: Journal
• Year: 2006
• Where: APAL
• Authors: John Krueger
• Keywords: APAL 2006, Partial Square Sequences, Stationary Sets, Stationary Subsets