TY - JOUR
T1 - The Magidor iteration and restrictions of ultrapowers to the ground model
AU - Kaplan, Eyal
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2025/2
Y1 - 2025/2
N2 - We study the Magidor iteration of Prikry forcings below a measurable limit of measurables κ. We first characterize all the normal measures κ carries in the generic extension, building on and extending the main result of [1]. Then, for every such normal measure, we prove that the restriction of its ultrapower, from the generic extension to the ground model, is an iterated ultrapower of V by normal measures. This is done without core model theoretic assumptions; GCH≤κ in the ground model suffices.
AB - We study the Magidor iteration of Prikry forcings below a measurable limit of measurables κ. We first characterize all the normal measures κ carries in the generic extension, building on and extending the main result of [1]. Then, for every such normal measure, we prove that the restriction of its ultrapower, from the generic extension to the ground model, is an iterated ultrapower of V by normal measures. This is done without core model theoretic assumptions; GCH≤κ in the ground model suffices.
UR - http://www.scopus.com/inward/record.url?scp=85207884383&partnerID=8YFLogxK
U2 - 10.1007/s11856-024-2674-1
DO - 10.1007/s11856-024-2674-1
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AN - SCOPUS:85207884383
SN - 0021-2172
VL - 265
SP - 605
EP - 660
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 2
ER -