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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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 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.

Article information

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

Dates
First available in Project Euclid: 23 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1358951101

Digital Object Identifier
doi:10.2178/jsl.7801060

Mathematical Reviews number (MathSciNet)
MR3087063

Zentralblatt MATH identifier
1268.03069

Citation

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. https://projecteuclid.org/euclid.jsl/1358951101


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