Existence of a Model of $o(\kappa )={\kappa }^{++}$ from Failure of GCH at a Measurable Cardinal

Abstract

It is well-known that the consistency strength of the GCH failing at a measurable cardinal is the existence of a cardinal $\kappa$ with $o(\kappa )={\kappa }^{++}$. As the literature does not contain more than a proof sketch of the lower bound of this equiconsistency, we give an expository proof which fills in the details in order to fill this gap in the literature.

arXiv comment2 pages