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Title: The Galvin property under the ultrapower axiom
Abstract We continue the study of the Galvin property from Benhamou, Garti, and Shelah (2023,Proceedings of the American Mathematical Society151, 1301–1309) and Benhamou (2023,Saturation properties in canonical inner models, submitted). In particular, we deepen the connection between certain diamond-like principles and non-Galvin ultrafilters. We also show that any Dodd sound nonp-point ultrafilter is non-Galvin. We use these ideas to formulate what appears to be the optimal large cardinal hypothesis implying the existence of a non-Galvin ultrafilter, improving on a result from Benhamou and Dobrinen (2023,Journal of Symbolic Logic, 1–34). Finally, we use a strengthening of the Ultrapower Axiom to prove that in all the known canonical inner models, a$$\kappa $$-complete ultrafilter has the Galvin property if and only if it is an iterated sum ofp-points.  more » « less
Award ID(s):
2346680
PAR ID:
10575805
Author(s) / Creator(s):
;
Publisher / Repository:
Cambridge Press
Date Published:
Journal Name:
Canadian Journal of Mathematics
ISSN:
0008-414X
Page Range / eLocation ID:
1 to 32
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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