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

Connor Watson

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arXiv · 2412.17660

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

Connor Watson

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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.

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Connor Watson. 2024-12-23. Existence of a Model of $o(\kappa)=\kappa^{++}$ from Failure of GCH at a Measurable Cardinal. https://arxiv.org/abs/2412.17660

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