Galvin’s conjecture and weakly precipitous ideals
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- by Todd Eisworth;
- Proc. Amer. Math. Soc.
- DOI: https://doi.org/10.1090/proc/17299
- Published electronically: June 30, 2025
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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 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].References
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Bibliographic Information
- Todd Eisworth
- Affiliation: Department of Mathematics, Ohio University, Athens, Ohio 45701
- MR Author ID: 629454
- ORCID: 0000-0003-4433-9463
- Email: eisworth@ohio.edu
- Received by editor(s): August 2, 2024
- Received by editor(s) in revised form: February 28, 2025
- Published electronically: June 30, 2025
- Additional Notes: This research was partly supported by NSF grant DMS-2400200.
- Communicated by: Vera Fischer
- © Copyright 2025 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
- MSC (2020): Primary 03E02, 03E55
- DOI: https://doi.org/10.1090/proc/17299