Journal of Symbolic Logic

A minimal Prikry-type forcing for singularizing a measurable cardinal

Peter Koepke, Karen Räsch, and Philipp Schlicht

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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 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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J. Symbolic Logic, Volume 78, Issue 1 (2013), 85-100.

First available in Project Euclid: 23 January 2013

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Koepke, Peter; Räsch, Karen; Schlicht, Philipp. A minimal Prikry-type forcing for singularizing a measurable cardinal. J. Symbolic Logic 78 (2013), no. 1, 85--100. doi:10.2178/jsl.7801060.

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