Extender-based Radin forcing
Author: Carmi Merimovich
Journal: Trans. Amer. Math. Soc. 355 (2003), 1729-1772
MSC (2000): Primary 03E35, 03E55
Published electronically: January 8, 2003
MathSciNet review: 1953523
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Abstract: We define extender sequences, generalizing measure sequences of Radin forcing.
Using the extender sequences, we show how to combine the Gitik-Magidor forcing for adding many Prikry sequences with Radin forcing.
We show that this forcing satisfies a Prikry-like condition, destroys no cardinals, and has a kind of properness.
Depending on the large cardinals we start with, this forcing can blow the power of a cardinal together with changing its cofinality to a prescribed value. It can even blow the power of a cardinal while keeping it regular or measurable.
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Affiliation: Computer Science Department, The Academic College of Tel-Aviv, 4 Antokolsky St., Tel-Aviv 64044, Israel
Keywords: Forcing, Radin forcing, extender, extender-based forcing, generalized continuum hypothesis, singular cardinal hypothesis
Received by editor(s): October 19, 1998
Published electronically: January 8, 2003
Additional Notes: This work is a part of research which, hopefully, will become the author’s Ph.D. thesis. It was done at Tel-Aviv University under the supervision of M. Gitik. The author thanks M. Gitik for his help with this work, with other works and just in general.
We thank Asaf Sharon for reading and pointing out some problems in a preliminary version of this work.
Article copyright: © Copyright 2003 American Mathematical Society