Small u(kappa) at singular kappa with compactness at kappa++

Radek Honzik; Sarka Stejskalova

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arXiv · 1910.14391

Small u(kappa) at singular kappa with compactness at kappa++

Radek Honzik·Sarka Stejskalova

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Abstract

We show that the tree property, stationary reflection and the failure of approachability at $κ^{++}$ are consistent with $\mathfrak{u}(κ) = κ^+ < 2^κ$, where $κ$ is a singular strong limit cardinal with the countable or uncountable cofinality. As a by-product, we show that if $λ$ is a regular cardinal, then stationary reflection at $λ^+$ is indestructible under all $λ$-cc forcings (out of general interest, we also state a related result for the preservation of club stationary reflection).

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BibTeX RIS

Radek Honzik, Sarka Stejskalova. 2019-10-31. Small u(kappa) at singular kappa with compactness at kappa++. https://arxiv.org/abs/1910.14391

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