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A characterisation of $ 0^\char93 $ in terms of forcing

Author(s): Sy D. Friedman
Journal: Proc. Amer. Math. Soc. 134 (2006), 1823-1824.
MSC (2000): Primary 03E40, 03E45, 03E55
Posted: December 2, 2005
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Abstract: We show that ``saturation'' of the universe with respect to forcing over $ L$ with partial orders on $ \omega_1$ is equivalent to the existence of $ 0^\char93 $.

References:

1.
Abraham, U. and Shelah, S. Forcing closed unbounded sets, J. Symbolic Logic 48 (1983) 643-657. MR 0716625 (85i:03112)

2.
Jech, T. Set Theory: Millenium Edition, Springer-Verlag, 2003. MR 1940513 (2004g:03071)

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Additional Information:

Sy D. Friedman
Affiliation: Kurt Gödel Research Center for Mathematical Logic, Währingerstrasse 25, A-1090 Wien, Austria
Email: sdf@logic.univie.ac.at

DOI: 10.1090/S0002-9939-05-08322-X
PII: S 0002-9939(05)08322-X
Keywords: Forcing, Silver indiscernibles, constructibility
Received by editor(s): January 4, 2005
Posted: December 2, 2005
Additional Notes: This research was supported by Research Project Number P16334-NO5 of the Austrian Foundation for the Support of Scientific Research (FWF). The author thanks David Asperò for posing the question answered here.
Communicated by: Carl G. Jockusch, Jr.
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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