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  1. (, Proceedings of the American Mathematical Society)
    We investigate a combinatorial game on ω<#comment/> 1 \omega _1 and show that mild large cardinal assumptions imply that every normal ideal on ω<#comment/> 1 \omega _1 satisfies a weak version of precipitousness. As an application, we show 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 [Forum Math. Pi 8 (2020), p. e15]. 
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    Free, publicly-accessible full text available June 30, 2026