The subcompleteness of diagonal Prikry forcing

Kaethe Minden

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arXiv · 1807.08782

The subcompleteness of diagonal Prikry forcing

Kaethe Minden

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Abstract

Let $D$ be an infinite discrete set of measurable cardinals. It is shown that generalized Prikry forcing to add a countable sequence to each cardinal in $D$ is subcomplete. To do this it is shown that a simplified version of generalized Prikry forcing which adds a point below each cardinal in $D$, called generalized diagonal Prikry forcing, is subcomplete. Moreover, the generalized diagonal Prikry forcing associated to $D$ is subcomplete above $\mu$, where $\mu$ is any regular cardinal below the first limit point of $D$.

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BibTeX RIS

Kaethe Minden. 2018-07-23. The subcompleteness of diagonal Prikry forcing. https://arxiv.org/abs/1807.08782

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