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arXiv · 1808.06390

The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps

Mohammad Golshani·Alejandro Poveda
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Abstract

Assuming the existence of a strong cardinal $\kappa$, a weakly compact cardinal $\lambda$ above it and $\gamma > \lambda,$ we force a generic extension in which $\kappa$ is a singular strong limit cardinal of any given cofinality $\delta$, $2^\kappa\geq \gamma$ and such that the tree property holds at $\kappa^{++}$.

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Mohammad Golshani, Alejandro Poveda. 2018-08-20. The tree property at double successors of singular cardinals of uncountable cofinality with infinite gaps. https://arxiv.org/abs/1808.06390

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