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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A minimal model for $ \neg{\rm CH}$: iteration of Jensen's reals


Author: Uri Abraham
Journal: Trans. Amer. Math. Soc. 281 (1984), 657-674
MSC: Primary 03E35; Secondary 03C62, 03E45, 03E50
DOI: https://doi.org/10.1090/S0002-9947-1984-0722767-0
MathSciNet review: 722767
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Abstract: A model of $ {\text{ZFC}} + {2^{\aleph_0}} = {\aleph_2}$ is constructed which is minimal with respect to being a model of $ \neg {\text{CH}}$. Any strictly included submodel of $ {\text{ZF}}$ (which contains all the ordinals) satisfies $ {\text{CH}}$. In this model the degrees of constructibility have order type $ {\omega_2}$. A novel method of using the diamond is applied here to construct a countable-support iteration of Jensen's reals: In defining the $ \alpha {\text{th}}$ stage of the iteration the diamond "guesses" possible $ \beta > \alpha $ stages of the iteration.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0722767-0
Article copyright: © Copyright 1984 American Mathematical Society

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