Extender-based Magidor-Radin forcing (Q532622)

From the author's introduction: ``The general theme of the forcing notion we present is as follows. Given a Mitchell increasing extender sequence, \(2^{\kappa}\) is controlled by the size of the extenders, the cofinality of \(\kappa\) is controlled by the length of the sequence, and a club is added to \(\kappa\) so that the power and cofinality of cardinals in the club is controlled by reflections of the extender sequence. In the generic extension \(\kappa\) can become singular, can remain regular, or measurable.'' The paper begins with the definition of extender-based Prikry forcing, which will play a role in the ultimate definition of extender-based Magidor-Radin forcing. The ideas used in the definition of Magidor-Radin forcing are then illustrated via extender-based Magidor forcing using two extenders. The reader is expected to be acquainted with large cardinals, especially with extenders, measures, and elementary embeddings, and of course with forcing.