Destroying Saturation while Preserving Presaturation at an Inaccessible; an Iterated Forcing Argument

Noah Schoem

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arXiv · 1909.06704

Destroying Saturation while Preserving Presaturation at an Inaccessible; an Iterated Forcing Argument

Noah Schoem

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Abstract

We prove that a large class of presaturated ideals at inaccessible cardinals can be de-saturated while preserving their presaturation, answering both a question of Foreman and of Cox and Eskew. We do so by iterating a generalized version of Baumgartner and Taylor's forcing to add a club with finite conditions along an inaccessible cardinal, and invoking Foreman's Duality Theorem.

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BibTeX RIS

Noah Schoem. 2019-09-15. Destroying Saturation while Preserving Presaturation at an Inaccessible; an Iterated Forcing Argument. https://arxiv.org/abs/1909.06704

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