TY - JOUR
T1 - Galvin’s property at large cardinals and an application to partition calculus
AU - Benhamou, Tom
AU - Garti, Shimon
AU - Poveda, Alejandro
N1 - Publisher Copyright:
© The Hebrew University of Jerusalem 2025.
PY - 2025
Y1 - 2025
N2 - In the first part of this paper we produce models where κ is certain very large cardinal and every ground model κ-complete ultrafilter extends to a non-Galvin one. In the opposite direction, we also produce such models but this time every ground model κ-complete ultrafilter extends to a P-point ultrafilter, hence to a Galvin one. Finally, we apply Galvin’s property to obtain consistently new instances of the classical problem in partition calculus λ → (λ, ω + 1)2 both in ZFC and ZF.
AB - In the first part of this paper we produce models where κ is certain very large cardinal and every ground model κ-complete ultrafilter extends to a non-Galvin one. In the opposite direction, we also produce such models but this time every ground model κ-complete ultrafilter extends to a P-point ultrafilter, hence to a Galvin one. Finally, we apply Galvin’s property to obtain consistently new instances of the classical problem in partition calculus λ → (λ, ω + 1)2 both in ZFC and ZF.
UR - http://www.scopus.com/inward/record.url?scp=105002164431&partnerID=8YFLogxK
U2 - 10.1007/s11856-025-2749-7
DO - 10.1007/s11856-025-2749-7
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AN - SCOPUS:105002164431
SN - 0021-2172
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
ER -