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IPM
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“School of Mathematics”

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Paper   IPM / M / 12780
School of Mathematics
  Title:   Killing the GCH everywhere with a single real
  Author(s):  M. Golshani (Joint with Sy-D. Friedman)
  Status:   Published
  Journal: J. Symbolic Logic
  Vol.:  78
  Year:  2013
  Pages:   803-823
  Supported by:  IPM
  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.

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