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An variation for one souslin tree

Published online by Cambridge University Press:  12 March 2014

Paul Larson
Paul Larson*
Affiliation:
Equipe de Logique, Université Paris VII, 2 Place Jussieu, Paris 75251, Cedex, France E-mail: larson@logique.jussieu.fr
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Abstract

We present a variation of the forcing as presented in Woodin [4], Our forcing is a ℙmax-style construction where each model condition selects one Souslin tree. In the extension there is a Souslin tree TG which is the direct limit of the selected Souslin trees in the models of the generic. In some sense, the generic extension is a maximal model of "there exists a minimal Souslin tree,” with TG being this minimal tree. In particular, in the extension this Souslin tree has the property that forcing with it gives a model of Souslin's Hypothesis.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 81 - 98
Copyright
Copyright © Association for Symbolic Logic 1999

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References

REFERENCES

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[4]Woodin, W.H., The axiom of determinacy, forcing axioms, and the nonstationary ideal, in preparation.Google Scholar