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March 2013 A minimal Prikry-type forcing for singularizing a measurable cardinal
Peter Koepke, Karen Räsch, Philipp Schlicht
J. Symbolic Logic 78(1): 85-100 (March 2013). DOI: 10.2178/jsl.7801060

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.

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Peter Koepke. Karen Räsch. Philipp Schlicht. "A minimal Prikry-type forcing for singularizing a measurable cardinal." J. Symbolic Logic 78 (1) 85 - 100, March 2013. https://doi.org/10.2178/jsl.7801060

Information

Published: March 2013
First available in Project Euclid: 23 January 2013

zbMATH: 1268.03069
MathSciNet: MR3087063
Digital Object Identifier: 10.2178/jsl.7801060

Rights: Copyright © 2013 Association for Symbolic Logic

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Vol.78 • No. 1 • March 2013
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