Galvin's Conjecture and Weakly Precipitous Ideals

2023/07/14 by Todd Eisworth, Eisworth, Todd
Computer Science · Mathematics · #03E02 #03E55 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2307.07369

openalex publication_date 2023/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate a combinatorial game on ω₁ and show that mild large cardinal assumptions imply that every normal ideal on ω₁ satisfies a weak version of precipitousness. As an application, we show that that the Raghavan-Todorčević 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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