Abstract
We continue the work done in [3], [1]. We prove that for every set A in a Magidor-Radin generic extension using a coherent sequence such that \({o^{\vec U}}\left( \kappa \right) < \kappa \), there is a subset C′ of the Magidor club such that V[A] = V[C′]. Also we classify all intermediate ZFC transitive models V ⊆ M ⊆ V[G].
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Acknowledgment
The authors would like to thank the referee for his careful examination of the paper and for many useful insights. Also they would like to thank the participants of the “Set Theory Seminar” of Tel-Aviv University for their comments during the presentation of this work.
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The work of the second author was partially supported by ISF grant No.1216/18.
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Benhamou, T., Gitik, M. Intermediate models of Magidor-Radin forcing. I. Isr. J. Math. 252, 47–94 (2022). https://doi.org/10.1007/s11856-022-2335-1
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DOI: https://doi.org/10.1007/s11856-022-2335-1