Journal of Symbolic Logic 78 (1):85-100 (2013)

Abstract
Recently, Gitik, Kanovei and the first author proved that for a classical Prikry forcing extension the family of the intermediate models can be parametrized by $\mathscr{P}(\omega)/\mathrm{finite}$. By modifying the standard Prikry tree forcing we define a Prikry-type forcing which also singularizes a measurable cardinal but which is minimal, i.e., there are \emph{no} intermediate models properly between the ground model and the generic extension. The proof relies on combining the rigidity of the tree structure with indiscernibility arguments resulting from the normality of the associated measures
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DOI 10.2178/jsl.7801060
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References found in this work BETA

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Δ12-Sets of Reals.Jaime I. Ihoda & Saharon Shelah - 1989 - Annals of Pure and Applied Logic 42 (3):207-223.
The Covering Lemma for L[U].A. J. Dodd & R. B. Jensen - 1982 - Annals of Mathematical Logic 22 (2):127-135.
Boolean Extensions and Measurable Cardinals.K. Kunen - 1971 - Annals of Mathematical Logic 2 (4):359.
DELTA ¹2-Sets of Reals.J. I. Ihoda - 1989 - Annals of Pure and Applied Logic 42 (3):207.

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Citations of this work BETA

Prikry forcing and tree Prikry forcing of various filters.Tom Benhamou - 2019 - Archive for Mathematical Logic 58 (7-8):787-817.
Non-Homogeneity of Quotients of Prikry Forcings.Moti Gitik & Eyal Kaplan - 2019 - Archive for Mathematical Logic 58 (5-6):649-710.
Intermediate Models of Magidor-Radin Forcing-Part II.Tom Benhamou & Moti Gitik - 2022 - Annals of Pure and Applied Logic 173 (6):103107.

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