The first measurable can be the first inaccessible cardinal

Abstract

In [8] the second and third authors showed that if the least inaccessible cardinal is the least measurable cardinal, then there is an inner model with $o(\hat{I}º)\ge 2$. In this paper we improve this to $o(\hat{I}º)\ge \hat{I}º+1$ and show that if $\hat{I}º$ is a $\hat{I}{º}^{++}$-supercompact cardinal, then there is a symmetric extension in which it is the least inaccessible and the least measurable cardinal.

14 pages; final version