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Internal consistency for embedding complexity

Published online by Cambridge University Press:  12 March 2014

Sy-David Friedman
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, Währingerstrasse 25, A-1090 Wien, Austria, E-mail: sdf@logic.univie.ac.at
Catherine Thompson
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, Währingerstrasse 25, A-1090 Wien, Austria, E-mail: aleph_nought@yahoo.com

Abstract

In a previous paper with M. Džamonja, class forcings were given which fixed the complexity (a universality covering number) for certain types of structures of size λ together with the value of 2λ for every regular λ. As part of a programme for examining when such global results can be true in an inner model, we build generics for these class forcings.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2008

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References

REFERENCES

[1]Beller, A., Jensen, R., and Welch, P., Coding the universe, London Mathematical Society Lecture Note Series, vol. 47, Cambridge University Press, Cambridge-New York, 1982.CrossRefGoogle Scholar
[2]Dobrinen, N. and Friedman, S., Internal consistency and co-stationarity of the ground model, this Journal, vol. 73 (2008), no. 2, pp. 512521.Google Scholar
[3]Džamonja, M., Friedman, S., and Thompson, K., Global complexity results, Set theory: Recent trends and applications (Andretta, A., editor), Quaderni di Matematica, vol. 17, 2007, Seconda Universita di Napoli, pp. 2545.Google Scholar
[4]Easton, W. B., Powers of regular cardinals, Annals of Mathematical Logic, vol. 1 (1970), pp. 139178.CrossRefGoogle Scholar
[5]Friedman, S., Fine structure and class forcing, de Gruyter, 2000.CrossRefGoogle Scholar
[6]Friedman, S., Internal consistency and the inner model hypothesis, The Bulletin of Symbolic Logic, vol. 12 (2006), no. 4, pp. 591600.CrossRefGoogle Scholar
[7]Friedman, S. and Ondrejović, P., Internal consistency of Easton's theorem, submitted, http://www.logic.univie.ac.at/~sdf/papers/.Google Scholar
[8]Friedman, S. and Thompson, K., Perfect trees and elementary embeddings, this Journal, vol. 73, no. 3, pp. 906918.Google Scholar
[9]Komjáth, P. and Shelah, S., Universal graphs without large cliques, Journal of Combinatorial Theory, vol. 63 (1995), no. 1, pp. 125135.CrossRefGoogle Scholar