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Global co-stationarity of the ground model from a new countable length sequence


Author: Natasha Dobrinen
Journal: Proc. Amer. Math. Soc. 136 (2008), 1815-1821
MSC (2000): Primary 03E05, 03E35, 03E65, 05C05
DOI: https://doi.org/10.1090/S0002-9939-08-09094-1
Published electronically: January 9, 2008
MathSciNet review: 2373613
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Abstract: Suppose $ V\subseteq W$ are models of ZFC with the same ordinals, and that for all regular cardinals $ \kappa$ in $ W$, $ V$ satisfies $ \square_{\kappa}$. If $ W\setminus V$ contains a sequence $ r:\omega\rightarrow\gamma$ for some ordinal $ \gamma$, then for all cardinals $ \kappa<\lambda$ in $ W$ with $ \kappa$ regular in $ W$ and $ \lambda\ge\gamma$, $ (\mathscr{P}_{\kappa}(\lambda))^W\setminus V$ is stationary in $ (\mathscr{P}_{\kappa}(\lambda))^W$. That is, a new $ \omega$-sequence achieves global co-stationarity of the ground model.


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Additional Information

Natasha Dobrinen
Affiliation: Kurt Gödel Research Center for Mathematical Logic, Währinger Strasse 25, 1090 Wien, Austria
Address at time of publication: Department of Mathematics, University of Denver, Denver, Colorado 80208
Email: dobrinen@logic.univie.ac.at. natasha.dobrinen@du.edu

DOI: https://doi.org/10.1090/S0002-9939-08-09094-1
Received by editor(s): November 20, 2006
Published electronically: January 9, 2008
Additional Notes: This work was supported by FWF grant P 16334-N05. The author wishes to thank Justin Moore for invaluable help and Paul Larson for direction
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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