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arXiv · 1802.07986

A Version of $κ$-Miller Forcing

Heike Mildenberger·Saharon Shelah
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Abstract

Let $κ$ be an uncountable cardinal such that $2^{<κ} = κ$ or just ${\rm cf}(κ) > ω$, $2^{2^{<κ}}= 2^κ$, and $([κ]^κ, \supseteq)$ collapses $2^κ$ to $ω$. We show under these assumptions the $κ$-Miller forcing with club many splitting nodes collapses $2^κ$ to $ω$ and adds a $κ$-Cohen real.

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Heike Mildenberger, Saharon Shelah. 2019-03-05. A Version of $κ$-Miller Forcing. https://arxiv.org/abs/1802.07986

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