Intermediate Models in Magidor-Radin Forcing- Part I

Abstract

We continue the work done by Gitik, Kanovei, Koepke, and later by the authors. We prove that for every set $A$ in a Magidor-Radin generic extension using a coherent sequence such that $o^{\vec{U}}(\kappa )<\kappa$, there is a subset $C^{\prime }$ of the Magidor club such that $V[A]=V[C^{\prime }]$. Also we classify all intermediate $ZFC$ transitive models $V\subseteq M\subseteq V[G]$.

Cited by in corpus (2)

• Intermediate Models of Magidor-Radin Forcing- Part II
• The Galvin property under the Ultrapower Axiom