Intermediate Models of Magidor-Radin Forcing- Part II

Abstract

We continue the work done by the authors and before that by the second author, Kanovei and koepke. We prove that for every set of ordinals $A$ in a Magidor-Radin generic extension using a coherent sequence such that $o^{\vec{U}}(\kappa )<{\kappa }^{+}$, there is $C^{\prime }\subseteq C_G$, such that $V[A]=V[C^{\prime }]$. Also we prove that the supremum of a fresh set in a Prikry, tree Prikry, Magidor, Radin-Magidor and Radin forcing, changes cofinality to $\omega$.

References in corpus (2)

• Sets in Prikry and Magidor Generic Extensions
• Intermediate Models in Magidor-Radin Forcing- Part I

Cited by in corpus (7)

• Negating the Galvin Property
• Kurepa trees and the failure of the Galvin property
• On Cohen and Prikry Forcing Notions
• Cofinal types of ultrafilters over measurable cardinals
• The Galvin property under the Ultrapower Axiom
• Non-Galvin Filters
• Galvin's property at large cardinals and an application to partition calculus