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arXiv · 2401.02757

The first measurable can be the first inaccessible cardinal

Moti Gitik·Yair Hayut·Asaf Karagila
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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 $o(\kappa)\geq2$. In this paper we improve this to $o(\kappa)\geq\kappa+1$ and show that if $\kappa$ is a $\kappa^{++}$-supercompact cardinal, then there is a symmetric extension in which it is the least inaccessible and the least measurable cardinal.

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Moti Gitik, Yair Hayut, Asaf Karagila. 2024-01-05. The first measurable can be the first inaccessible cardinal. https://arxiv.org/abs/2401.02757

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