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A power function with a fixed finite gap everywhere

Published online by Cambridge University Press:  12 March 2014

Carmi Merimovich
Carmi Merimovich*
Affiliation:
Computer Science Department, Tel-Aviv Academic College, 4 Antokolsky St., Tel-Aviv 64044, Israel, E-mail: carmi@mta.ac.il
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Abstract

We give an application of the extender based Radin forcing to cardinal arithmetic. Assuming κ is a large enough cardinal we construct a model satisfying 2κ = κ+n together with 2λ = λ+n for each cardinal λ < κ, where 0 < n < ω. The cofinality of κ can be set arbitrarily or κ can remain inaccessible.

When κ remains an inaccessible, Vκ is a model of ZFC satisfying 2λ = λ+n for all cardinals λ.

Keywords

Forcingmodified Radin forcingextenderextender based forcinggeneralized continuum hypothesissingular cardinal hypothesis
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 72 , Issue 2 , June 2007 , pp. 361 - 417
Copyright
Copyright © Association for Symbolic Logic 2007

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