Intermediate Models in Magidor-Radin Forcing- Part I

Tom Benhamou; Moti Gitik

Intermediate Models in Magidor-Radin Forcing- Part I

Logic 2022-03-03 v3

Authors: Tom Benhamou , Moti Gitik

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 $C'$ of the Magidor club such that $V[A]=V[C']$ . Also we classify all intermediate $ZFC$ transitive models $V\subseteq M\subseteq V[G]$ .

Cite

@article{arxiv.2009.12775,
  title  = {Intermediate Models in Magidor-Radin Forcing- Part I},
  author = {Tom Benhamou and Moti Gitik},
  journal= {arXiv preprint arXiv:2009.12775},
  year   = {2022}
}