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arXiv · 2307.07369

Galvin's Conjecture and Weakly Precipitous Ideals

Todd Eisworth
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Abstract

We investigate a combinatorial game on $\omega_1$ and show that mild large cardinal assumptions imply that every normal ideal on $\omega_1$ satisfies a weak version of precipitousness. As an application, we show that that the Raghavan-Todor\v{c}evi\'{c} proof of a longstanding conjecture of Galvin (done assuming the existence of a Woodin cardinal) can be pushed through under much weaker large cardinal assumptions.

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Todd Eisworth. 2023-07-14. Galvin's Conjecture and Weakly Precipitous Ideals. https://arxiv.org/abs/2307.07369

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