2022/12/28 by Tom Benhamou, Benhamou, Tom
Mathematics · Computer Science · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2212.14096
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 κ-complete ultrafilter over a measurable cardinal κ satisfies the Galvin property. On the other hand, we prove that supercompact cardinals always carry non-Galvin κ-complete ultrafilters. Finally, we prove that \diamondsuit(κ) implies the existence of a κ-complete filter which extends the club filter and fails to satisfy the Galvin property. This answers questions \cite[Question 5.22]TomMotiII,\cite[Question 3.4]Non-GalvinFil and questions ,\cite[Question 4.5]BenGarShe,\cite[Question 2.26]bgp.