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Internal consistency and global co-stationarity of the ground model

Published online by Cambridge University Press:  12 March 2014

Natasha Dobrinen  and
Sy-David Friedman
Natasha Dobrinen*
Affiliation:
Universität Wien, Kurt Gödel Research Center for Mathematical Logic, Währinger Straße 25, 1090 Wien, Austria
Sy-David Friedman
Affiliation:
Universität Wien, Kurt Gödel Research Center for Mathematical Logic, Währinger Straße 25, 1090 Wien, Austria, E-mail: [email protected], URL: http://www.logic.univie.ac.at/~sdf/
*
University of Denver, Department of Mathematics, 2360 S Gaylord St., Denver, CO 80208, USA, E-mail: [email protected], URL: http://www.math.du.edu/dobrinen/
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Abstract

Global co-stationarity of the ground model from an ℵ2-c.c. forcing which adds a new subset of ℵ1 is internally consistent relative to an ω1-Erdős hyperstrong cardinal and a sufficiently large measurable above.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 2 , June 2008 , pp. 512 - 521
Copyright
Copyright © Association for Symbolic Logic 2008

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References

REFERENCES

[1]Baumgartner, James E., On the size of closed unbounded sets, Annals of Pure and Applied Logic, vol. 54 (1991), pp. 195–227.CrossRefGoogle Scholar
[2]Beller, A., Jensen, R., and Welch, P., Coding the Universe, Cambridge University Press, 1982.CrossRefGoogle Scholar
[3]Dobrinen, Natasha and Friedman, Sy-David, Co-stationarity of the ground model, this Journal, vol. 71 (2006), no. 3, pp. 1029–1043.Google Scholar
[4]Friedman, Sy-David, Internal consistency and the inner model hypothesis, The Bulletin of Symbolic Logic, vol. 12 (2006), no. 4, pp. 591–600.CrossRefGoogle Scholar
[5]Koppelberg, Sabine, Handbook of Boolean Algebra, vol. 1, North-Holland, 1989.Google Scholar
[6]Kueker, David W., Löwenheim-Skolem and interpolation theorems in infinitary languages, Bulletin of the American Mathematical Society, vol. 78 (1972), pp. 211–215.CrossRefGoogle Scholar
[7]Menas, Telis K., On strong compactness and supercompactness, Annals of Mathematical Logic, vol. 7 (1974/1975), pp. 327–359.CrossRefGoogle Scholar