Changing cofinalities and the nonstationary ideal (Q1105593): Difference between revisions

The paper consists of two parts. The first part is of technical character: the author introduces an iterated forcing of Prikry type. In the second part he applies the method introduced in the first part to the study of the ideal of nonstationary sets on a cardinal. The main result is the following theorem: If there is a ``very large'' cardinal \(\kappa\), then there is a forcing notion \({\mathbb{P}}\) such that in \(V^{{\mathbb{P}}}\) there is a stationary set S on \(\kappa\) with the property that forcing with \(NS_{\kappa}| S\) (nonstationary sets on \(\kappa\) restricted to S) preserves the cardinals, does not add bounded subsets of \(\kappa\) and for every regular \(\alpha <\kappa\) there is a forcing condition which forces ``cf \(\kappa\) \(=\alpha ''\).