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Killing The GCH Everywhere with a Single Real

Published online by Cambridge University Press:  12 March 2014

Sy-David Friedman  and
Mohammad Golshani
Sy-David Friedman
Affiliation:
Kurtgódel Research center, University of Vienna, Vienna, Austria, E-mail: sdf@logic.univie.ac.at
Mohammad Golshani
Affiliation:
Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran School of Mathematics, Institute of Research in Fundamental Sciences (IPM), P.O.BOX:19395-5746, Tehran, Iran, E-mail: golshani.m@gmail.com
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Abstract

Shelah-Woodin [10] investigate the possibility of violating instances of GCH through the addition of a single real. In particular they show that it is possible to obtain a failure of CH by adding a single real to a model of GCH, preserving cofinalities. In this article we strengthen their result by showing that it is possible to violate GCH at all infinite cardinals by adding a single real to a model of GCH. Our assumption is the existence of an H(κ+3)-strong cardinal; by work of Gitik and Mitchell [6] it is known that more than an H(κ++)-strong cardinal is required.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 3 , September 2013 , pp. 803 - 823
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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