Saturation properties of ultrafilters in canonical inner models
Tom Benhamou · Journal of Mathematical Logic · 2025
In this paper, we improve Galvin’s Theorem for ultrafilters which are p-point limits of p-points. This implies that in all the canonical inner models up to a superstrong cardinal, every [Formula: see text]-complete ultrafilter over a measurable cardinal [Formula: see text] satisfies the Galvin property. On the other hand, we prove that supercompact cardinals always carry non-Galvin [Formula: see text]-complete ultrafilters. Finally, we prove that [Formula: see text] implies the existence of a [Formula: see text]-complete filter which extends the club filter and fails to satisfy the Galvin property. This answers questions [ 8 , Question 5.22], [ 4 , Question 3.4] and questions, [ 7 , Question 4.5], [ 6 , Question 2.26].